Artículo
Properties of Poincaré half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems
Autor/es | Carmona Centeno, Victoriano
Fernández Sánchez, Fernando García Medina, Elisabeth |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Fecha de publicación | 2023 |
Fecha de depósito | 2023-09-07 |
Publicado en |
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Resumen | This paper deals with fundamental properties of Poincaré half-maps defined
on a straight line for planar linear systems. Concretely, we focus on the analyticity
of the Poincaré half-maps, their series expansions (Taylor ... This paper deals with fundamental properties of Poincaré half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincaré half-maps, their series expansions (Taylor and Newton–Puiseux) at the tangency point and at infinity, the relative position between the graph of Poincaré half maps and the bisector of the fourth quadrant, and the sign of their second derivatives. All these properties are essential to understand the dynamic behavior of planar piece wise linear systems. Accordingly, we also provide some of their most immediate, but non-trivial, consequences regarding periodic orbits |
Agencias financiadoras | Ministerio de Ciencia, Innovación y Universidades (MICINN). España Ministerio de Economía y Competitividad (MINECO). España Consejería de Educación y Ciencia. Junta de Andalucía Consejería de Economía, Conocimiento, Empresas y Universidad. Junta de Andalucía |
Identificador del proyecto | PGC2018-096265-B-I00
PID2021-123200NB-I00 TIC-0130 P12-FQM-1658 US-1380740 P20-01160 |
Cita | Carmona Centeno, V., Fernández Sánchez, F. y García Medina, E. (2023). Properties of Poincaré half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems. Electronic Journal of Qualitative Theory of Differential Equations, 22. https://doi.org/10.14232/ejqtde.2023.1.22. |
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