Artículos (Matemática Aplicada II)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10899

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Numerical study of a Belyakov degenerate T-point in the Lorenz system
(Elsevier, 2026) Algaba Durán, Antonio; Merino Morlesin, Manuel; Rodríguez Luis, Alejandro José; Matemática Aplicada II; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Junta de Andalucía
In this work we find a T-point in the Lorenz system, a codimension-two heteroclinic cycle connecting the origin and the nontrivial equilibria, in a region of parameter space where all three equilibria are real saddles. By moving a third parameter, this (principal) T-point undergoes a degeneracy because the nontrivial equilibria go from real saddles to saddle-foci. The numerical study of this previously unknown codimension-three global bifurcation, which we name Belyakov T-point, shows that it is an important organizing center. In its neighborhood, among other codimension-two bifurcations, we find Belyakov degenerate homoclinic and heteroclinic connections to the nontrivial equilibria, sequences of subsidiary T-points and, most notably, an infinite sequence of type C inclination-flip homoclinic orbits to the origin. Thus, we have found a codimension-three global bifurcation from which curves of inclination-flip degeneracies emerge. In addition, other codimension-three degeneracies, such as T-point-Hopf bifurcations, have also been detected. The first two elements of a sequence of Belyakov subsidiary T-points are found, too.
Bogdanov–Takens Bifurcation in a Bidirectional DC–DC Converter Supplying a Constant Power Load
(Institute of Electrical and Electronics Engineers (IEE), 2026) Torres Peral, Francisco; Freire Macías, Emilio; Benadero, Luis; Sebastiá-Rullo, Max; Mandal, Kuntal; El Aroudi, Abdelali; Matemática Aplicada II; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Ministry of Research and Universities of the Government of Catalonia
Over the decades, bifurcation theory has emerged as a significant area of research, providing deep insights into the complex dynamics of systems across multiple disciplines. Moreover, it serves as a foundation for devising effective control methodologies aimed at avoiding or delaying undesirable dynamical transitions. This paper deals with both local and global dynamics of a bidirectional dc-dc boost converter supplying a constant power load (CPL) with a stabilizing resistor inserted in series with the main inductor. Numerical simulations performed on the averaged model of the system show interesting bifurcation phenomena explaining its local and global dynamical behavior. In particular, it is shown that in some parametric region, the system has two coexisting equilibria, one of them being a saddle and the other one an anti-saddle. The latter can be stable or unstable. An unstable limit cycle also coexists with the stable anti-saddle equilibrium. This limit cycle disappears through a homoclinic bifurcation. Moreover, a parameter space reduction is carried out by choosing suitable bifurcation parameters, and the normal form of the Bogdanov-Takens bifurcation is obtained hence mathematically demonstrating its existence. Finally, the analytical and simulation results on the switched model are partially validated by experimental measurements from a laboratory prototype.
General order virtual element approximation for the Smagorinsky turbulence model
(Elsevier, 2026-11) Berrone, Stefano; Cascavita, Karol L; Delgado Ávila, Enrique; Rubino, Samuele; Strazzullo, Maria; Vicini, Fabio; Matemática Aplicada II; Ecuaciones Diferenciales y Análisis Numérico; Ministerio de Ciencia e Innovación (MICIN). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
In this paper, we investigate a Smagorinsky model in a virtual element framework to simulate convection-dominated Navier–Stokes equations. We conduct a two-dimensional numerical investigation to assess the performance of the general order virtual element approximation in this context. First, we examine numerically the convergence of the method with respect to the meshsize to certify the novel virtual element numerical discretization, which includes, for the first time, a discretization of the Smagorinsky term. Moreover, we present a numerical study of a lid-driven cavity for different Reynolds numbers (up to 10000) and meshes (uniform, anisotropic, and isotropic with hanging nodes). The results highlight the main advantage of using the virtual elements method in this context: the isotropic refinement with hanging nodes enhances the accuracy of the solution compared to the anisotropic mesh, uses fewer degrees of freedom with respect to the uniform mesh, and yields the most stable behavior in terms of convergence of the Newton solver.
MASPA: An efficient strategy for path planning with a tethered marsupial robotics system
(Elsevier, 2026-12-15) Capitán Fernández, Jesús; Díaz Báñez, José Miguel; Pérez Cutiño, Miguel Ángel; Rodríguez Sánchez, Fabio; Ventura Molina, Inmaculada; Ingeniería de Sistemas y Automática; Matemática Aplicada II; Ministerio de Ciencia e Innovación (MICIN). España; European Commission (EC); TEP995: Multi-Robot and Control Systems; FQM413: Research Group on Geometric Algorithms & Applications
A marsupial robotics system comprises three components: an Unmanned Ground Vehicle (UGV), an Unmanned Aerial Vehicle (UAV), and a tether connecting both robots. Marsupial systems are highly beneficial in industry as they extend the UAV’s battery life during flight. This paper introduces a novel strategy for a specific path planning problem in marsupial systems, where each of the components must avoid collisions with ground and aerial obstacles modeled as 3D cuboids. Given an initial configuration in which the UAV is positioned atop the UGV, the goal is to reach an aerial target with the UAV. We assume that the UGV first moves to a position from which the UAV can take off and fly through a vertical plane to reach the aerial target. We propose an approach that discretizes the space to approximate an optimal solution, minimizing the sum of the lengths of the ground and air paths. First, we assume a taut tether and use a novel algorithm that leverages the convexity of the tether and the geometry of obstacles to efficiently determine the locus of feasible take-off points for the UAV. We then apply this result to scenarios that involve loose tethers. Simulation results show that our approach can solve complex situations in seconds, outperforming baseline planning methods based on RRT (Rapidly-exploring Random Trees).
On the Rates of Convergence of Orbits in Semigroups of Holomorphic Functions
(2026-04-07) Betsakos, Dimitrios; Cruz Zamorano, Francisco José; Zarvalis, Konstantinos; Matemática Aplicada II; Ministerio de Ciencia e Innovación (MICIN). España; Agencia Estatal de Investigación. España
Let (φt) be a continuous semigroup of holomorphic self-maps ofthe unit diskDwith Denjoy–Wolff pointτ∈D. We study the rate of con-vergence of the forward orbits of (φt) to the Denjoy–Wolff point by findingexplicit bounds for the quantity|φt(z)−τ|,z∈D,t >0. We further discussthe corresponding rate of convergence for the backward orbits of (φt)
A problem on spaces of holomorphic maps and the geometry of image domains
(2026-03-12) Cruz Zamorano, Francisco José; Matemática Aplicada II; Ministerio de Ciencia e Innovación (MICIN). España; Agencia Estatal de Investigación. España
We present an old problem in Geometric Function Theory: characterizing the domains Ω ⊂ ℂ for which every holomorphic map from the unit disk into Ω must belong to a specific function space X. We will provide some generalities about this problem, although the main aim is to delve into the geometric characterizations for several classical spaces, such as the Bloch space , the spaces of analytic functions of bounded mean oscillation BMOA, the Nevanlinna class N, the Smirnov class N+, the Hardy spaces Hp, and the weighted Bergman spaces Ap 𝛼 . This work synthesizes a number of seminal results by several authors, aiming to provide a unified introduction to this classical but active topic.
The Euclidean k-matching problem is NP-hard
(Elsevier, 2026-12) Díaz Báñez, José Miguel; Fabila Monroy, Ruy; Higes López, José Manuel; Marín Nevárez, Jesús Nestaly; Pérez Cutiño, Miguel Ángel; Pérez Lantero, Pablo; Matemática Aplicada II; Agencia Estatal de Investigación. España; European Union (UE); Universidad Autónoma de México (UNAM); FQM413: Research Group on Geometric Algorithms & Applications
Let G be a complete edge-weighted graph on n vertices. To each subset of vertices of G assign the cost of the minimum spanning tree of the subset as its weight. Suppose that n is a multiple of some fixed positive integer k. The k-matching problem is the problem of finding a partition of the vertices of G into k-sets (sets of k elements), that minimizes the sum of the weights of the k-sets. The case of k = 3 has been shown to be NP-hard [Johnsson et al., 1998]. In the Euclidean version, the vertices of G are points in the plane and the weight of an edge is the Euclidean distance between its endpoints. We call this problem the Euclidean k-matching problem. We show that, for every fixed k ≥ 3, the Euclidean k-matching problem is NP-hard. This resolves an open problem in the literature and provides the first theoretical justification for the use of known heuristic methods in the case of k =3. We also show that the problem remains NP-hard if the trees are required to be paths.
The 2-Shapley value for bicooperative games
(Springer, 2026-05-12) Jiménez Losada, Andrés; Basallote Galván, Manuela; Gallego Sánchez, Inés Magdalena; Jiménez Losada, Andrés; Matemática Aplicada II; Didáctica de las Matemáticas; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; FQM237: Juegos con Estructuras Combinatorias y de Orden; FQM226: Grupo de Investigación en Educación Matemática
In this paper, we propose a new Shapley-type value (the 2-Shapley value) for bico- operative games. Unlike classical cooperative games, bicooperative games assign values to pairs of disjoint coalitions (bicoalitions) representing players who support change and those who defend the status quo, while the remaining players abstain. To develop this new value, we employ antimatroid theory not as a structural constraint on the games, but as a methodological bridge. Specifically, we demonstrate that any bicooperative coalition structure is isomorphic to a specific antimatroid, which we term the ‘double antimatroid’. Leveraging this mathematical connection, we propose a new Shapley value, provide an axiomatization that preserves its fundamental axioms, and establish its consistency with existing solution concepts. Finally, we illustrate our theoretical proposal and the calculation of this value through an example modeling a decision-making process. This work provides a robust mathematical foundation connecting both structures, opening new perspectives for analysis within bicooperative game theory.
Computing Optimal Trajectories for a Tethered Pursuer in Straight-Line Motion
(Springer, 2026-06) Barrera Vicent, Aurelio; Díaz Báñez, José Miguel; Rodríguez, Fabio; Sánchez Canales, Vanesa; Matemática Aplicada II
In this paper, we address a trajectory planning problem for a marsupial robotic system composed of a ground robot and an aerial robot (drone) connected by a taut tether with maximum length L. We consider a scenario where both robots move along parallel lines in a vertical plane. The drone follows a predefined back-and-forth trajectory at constant speed, and the goal is to determine an optimal path for the ground robot. Specifically, we seek a minimum-link trajectory–a back-and-forth path with the fewest direction changes–and a constant speed for the ground robot such that the distance between the two robots never exceeds L. This problem can be framed within the context of a pursuit-evasion game, where the evader’s trajectory is known, and the goal is to compute an optimal trajectory for the pursuer. Employing geometric modeling techniques, we develop an optimal algorithm to compute a parameterized minimum-link trajectory for the ground-based pursuer, given the a priori known trajectory of the aerial evader. In addition, we solve three interconnected geometric optimization problems by systematically exploiting their inherent relationships.
Convergence on the boundary for iterates of holomorphic self-maps of the unit disk
(Springer, 2026-04-09) Betsakos, Dimitrios; Contreras Márquez, Manuel Domingo; Díaz Madrigal, Santiago; Matemática Aplicada II; Universidad de Sevilla; FQM133: Grupo de Investigación en Análisis Funcional
The study of iterated functions is fundamental in complex dynamics. For a holomorphic self-map ϕ of the unit disk D, the Denjoy–Wolff theorem (1926) establishes a key convergence property: if ϕ is not an elliptic automorphism, then its sequence of iterates, (ϕ ◦n), converges uniformly on compact subsets to a point τ ∈ D, called the Denjoy–Wolff point of ϕ. A related question concerns the behavior of these iterates at the boundary. By Fatou’s theorem, all functions ϕ ◦n have non-tangential limits at almost every point on the boundary of the unit disk.We denote these non-tangential limits as (ϕ ◦n) ∗. The behavior of the sequence ((ϕ ◦n) ∗) depends significantly on whether ϕ is an inner function or not.When ϕ is an inner function, the behaviour of ((ϕ ◦n) ∗ ) is wellestablished and can be found in texts by Aaronson or Doering and Mañé. However, when ϕ is not an inner function, the problem was not solved. Previous partial results have been contributed by Bourdon, Matache, and Shapiro; by Poggi-Corradini; and by Contreras, Díaz-Madrigal, and Pommerenke. In this paper, we achieved the final solution: if ϕ is not an inner function, then the sequence ((ϕ ◦n) ∗ ) converges to τ for almost every point on ∂D. Our technique also provides general results on nonautonomous iteration of holomorphic self-maps of the unit disk.
Lebesgue spaces with variable unbounded exponent: the finite measure case
(Elsevier, 2026-08) Mayoral Masa, Fernando; Matemática Aplicada II; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Agencia Estatal de Investigación. España; Junta de Andalucía
We study the variable exponent Lebesgue spaces Lp(·) (µ) in the case where the exponent p(·) is unbounded and the measure μ is finite. In this case, the subspace of elements with absolutely continuous norm and the closure of the simple functions play an important role in the study of copies of c0 and ℓ∞, in the properties of the embeddings and in the characterizations of the spaces obtained when the two Calderón complex interpolation methods are applied. Under appropriate conditions, we prove that the first complex interpolation method [·, ·][θ] applied to a couple (Lp0(·) (µ), Lp1(·) (µ)) is different from the corresponding Lpθ(·) (µ) unless the intermediate exponent pθ(·) is bounded
Juegos para enseñar estrategias a estudiantes de Secundaria y Bachillerato
(Federación Iberoamericana de Sociedades de Educación Matemática (FISEM), 2020-08-31) Núñez Valdés, Juan; Benavent, Jaume; Márquez Martínez, Alfonso; Geometría y Topología
El objetivo principal de este artículo es mostrar algunos juegos de estrategia a los profesores de Matemáticas de los niveles de Secundaria y Bachillerato, para que estos puedan trabajarlos en sus clases de una manera amena, motivadora y dinamizadora, que les permita conseguir la atención de sus alumnos y despertar en ellos el gusto e interés por la asignatura. Se muestran diez de estos juegos, dándose de cada uno de ellos una breve descripción y un ejemplo sencillo de su aplicación y se comentan los beneficios didácticos que se derivarían de su utilización.
On Lexp and L log L Zygmund's spaces and its r-convexifications: the Orlicz-Luxemburg point of view
(Springer, 2025-05) Mayoral Masa, Fernando; Matemática Aplicada II; Junta de Andalucía
The present paper is devoted to obtain numerical estimations for the equivalences between the Hardy–Littlewood norms of Zygmund’s spaces, Lexp and L log L, and the Luxemburg norms associated to concrete Young functions that define these spaces. Moreover, for a (finite) measure we compute the equivalence constants between the Hardy–Littlewood norms of Zygmund’s spaces and the norms as associate (Köthe-dual) spaces. It is also proved that, for each 0 < r < 1 the quasinorm of the r-convexification Lrexp of Lexp is equivalent to a norm. In the opposite, the quasinorm of the r-convexification Lr log L, of L log L, is not equivalent to a norm. In the atomic case, the r-convexification Lr log L has a separating dual. We analyse the weak compactness of the multiplication operators from L∞ to Lexp and from L log L to L1. From the weak compactness of the embeddings follows the reflexivity of certain Lions–Peetre interpolated spaces.
The Bispectral Problem, the Darboux Process, Monodromy and the Hermite Operator
(Springer, 2026-02-28) Castro Smirnova, Mirta María; Grünbaum, Francisco Alberto; Matemática Aplicada II; FQM262: Teoría de la Aproximación
The complete solution of the bispectral problem for the Schrödinger operator L = −d²/dx² + V(x) in [19] is obtained by the application of the Darboux process to the cases of V = 0 and V(x) = − 1/4x² . Both of these cases are trivially bispectral and after repeated applications of the Darboux process one gets either a pair of rank one bundles of bispectral situations (when starting from V = 0) or a rank two bispectral bundle (when starting from V(x) = − 1/4x² ). In the first case all operators have “trivial monodromy” as defined in [19]. In the second case the monodromy group of all operators is given by the integers. In this paper we start from V(x) = x², use the Darboux process and explore the connection between the rank of certain non-polynomial bispectral families and trivial monodromy by means of examples. The main conclusion is that the results in [19] do not apply verbatim in this case.
The slope problem in discrete iteration
(AMS, 2024-11-21) Contreras Márquez, Manuel Domingo; Cruz Zamorano, Francisco José; Rodríguez Piazza, Luis; Análisis Matemático; FQM104: Análisis Matemático
The slope problem in holomorphic dynamics in the unit disk goes back to Wolff in 1929. However, there have been several contributions to this problem in the last decade. In this article the problem is revisited, comparing the discrete and continuous cases. Some advances are derived in the discrete parabolic case of zero hyperbolic step, showing that the set of slopes has to be a closed interval which is independent of the initial point. The continuous setting is used to show that any such interval is a possible example. In addition, the set of slopes of a family of parabolic function is discussed, leading to examples of functions with some regularity whose set of slopes is non-trivial.
Boundedness properties for Sobolev inner products
(Elsevier, 2003-04-02) Castro Smirnova, Mirta María; Durán Guardeño, Antonio José; Matemática Aplicada II; FQM262: Teoría de la Aproximación
Abstract Sobolev orthogonal polynomials with respect to measures supported on subsets of the complex plane are considered. The connection between the following properties is studied: the multiplication operator Mp(z)=zp(z) defined on the space P of algebraic polynomials with complex coefficients is bounded with respect to the norm defined by the Sobolev inner product, the supports of the measures are compact and the zeros of the orthogonal polynomials lie in a compact subset of the complex plane. In particular, we prove that the boundedness of the multiplication operator M always implies the compactness of the supports.
Study of a homoclinic canard explosion from a degenerate center
(Elsevier, 2022-10) Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez Luis, Alejandro José; Matemática Aplicada II; Ministerio de Economía y Competitividad (MINECO). España; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Junta de Andalucía; National Natural Science Foundation of China
Canard explosion is an appealing event occurring in singularly perturbed systems. In this phenomenon, upon variation of a parameter within an exponentially small range, the amplitude of a small limit cycle increases abruptly. In this letter we analyze the canard explosion in a limit cycle related to a degenerate center (with zero Jacobian matrix). We provide a second-order approximation of the critical value of the parameter for which the canard explosion occurs. Numerical results are compared with the analytical predictions and excellent agreements are found. As in this problem the canard explosion ends in a homoclinic connection, a very good approximation for the homoclinic curve in the parameter plane is also obtained.
Memory effects in a vibrated thin granular layer
(EDP Sciences, 2025-12-01) Vega Reyes, Francisco; Rodríguez Rivas, Álvaro; García de Soria Lucena, María Isabel; Maynar Blanco, Pablo; Física Atómica, Molecular y Nuclear; Matemática Aplicada II; Física Aplicada I
We present in this work the first experimental evidence of the termal memory effect in agran-ular fluid. In particular, we observe here the Kovacs memory effect (an anomalous evolution of at least one macroscopic variable) in the granular temperatura of the fluidized granular monolayer. The experimental set-up consists here in a vertically shaken granular monolayer. The evolution of the granular temperatura curves clearly displays the characteristic Kovacs humps. Furthermore, it appears that, at experimental level, the shaken monolayer displays the so-called anomalous Kovacs effec; i. e., and upwards hump for cool down protocol (or a downwards hump for a heating up process). The experimental results are also supported by molecular dynamics simulation data which use a realisti ccomputational model for both the dynamics and tribology properties of the oscillatory top and bottom walls that are present in our laboratory.
Topological Loewner theory on Riemann surfaces
(Elsevier, 2021-01) Contreras Márquez, Manuel Domingo; Díaz Madrigal, Santiago; Matemática Aplicada II; European Union; FQM133: Grupo de Investigación en Análisis Funcional
We prove that topological evolution families on a Riemann surface S are rather trivial unless S is conformally equivalent to the unit disc or the punctuated unit disc. We also prove that, except for the torus where there is no non-trivial continuous Loewner chain, there is a topological evolution family associated to any topological Loewner chain and, conversely, any topological evolution family comes from a topological Loewner chain on the same Riemann surface.
Asymptotic behavior of orbits of holomorphic semigroups
(Elsevier, 2020-01) Bracci, Filippo; Contreras Márquez, Manuel Domingo; Díaz Madrigal, Santiago; Gaussier, Hervé; Zimmer, Andrew; Matemática Aplicada II; Ministerio de Economía y Competitividad (MINECO). España; FQM133: Grupo de Investigación en Análisis Funcional
Let (ϕt) be a holomorphic semigroup of the unit disc (i.e., the flow of a semicomplete holomorphic vector field) without fixed points in the unit disc and let Ω be the starlike at infinity domain image of the Koenigs function of (ϕt). In this paper we characterize the type of convergence of the orbits of (ϕt) to the Denjoy-Wolff point in terms of the shape of Ω. In particular we prove that the convergence is non-tangential if and only if the domain Ω is “quasi-symmetric with respect to vertical axis”. We also prove that such conditions are equivalent to the curve [0,∞)∋t↦ϕt(z) being a quasi-geodesic in the sense of Gromov. Also, we characterize the tangential convergence in terms of the shape of Ω.

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