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Tesis Doctoral
Robustness of nonuniform and random exponential dichotomies with applications to differential equations
(2022-03-17)
In this thesis, we study hyperbolicity for deterministic and random nonautonomous dynamical systems and their applications to differential equations. More precisely, we present results in the following topics: nonuniform ...
Capítulo de Libro
Attracting complex networks
(Springer, 2016)
Real phenomena from different areas of Life Sciences can be described by complex networks, whose structure is usually determining their intrinsic dynamics. On the other hand, Dynamical Systems Theory is a powerful tool for ...
Artículo
The stability of attractors for non-autonomous perturbations of gradient-like systems
(Elsevier, 2007-03-15)
We study the stability of attractors under non-autonomous perturbations that are uniformly small in time. While in general the pullback attractors for the nonautonomous problems converge towards the autonomous attractor ...
Artículo
Global Attractors for Multivalued Random Dynamical Systems
(2002)
We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the cocycle property. We show how this is a suitable framework for the study of the asymptotic behaviour ...
Artículo
Stabilisation of differential inclusions and PDEs without uniqueness by noise
(2008)
We prove that the asymptotic behaviour of partial differential inclusions and partial differential equations without uniqueness of solutions can be stabilised by adding some suitable Itˆo noise as an external perturbation. ...
Artículo
Existence and regularity of the pressure for the stochastic Navier-Stokes equations
(Springer, 2003-10)
We prove, on one hand, that for a convenient body force with values in the distribution space (H−1(D))d, where D is the geometric domain of the fluid, there exist a velocity u and a pressure p solution of the stochastic ...
Artículo
Structure of the pullback attractor for a non-autonomous scalar differential inclusion
(American Institute of Mathematical Sciences, 2016-08)
The structure of attractors for differential equations is one of the main topics in the qualitative theory of dynamical systems. However, the theory is still in its infancy in the case of multivalued dynamical systems. ...
Artículo
Stability, instability, and bifurcation phenomena in non-autonomous differential equations
(IOPscience, 2002-05)
There is a vast body of literature devoted to the study of bifurcation phenomena in autonomous systems of differential equations. However, there is currently no well-developed theory that treats similar questions for the ...
Artículo
The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations
(ScienceDirect, 2021-01-01)
In this work, we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, we study robustness and existence of exponential dichotomies ...