Published September 7, 2023
| Version v1
Publication
Properties of Poincaré half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems
Contributors
Others:
- Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
- Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería.
- 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
Description
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
Abstract
The Electronic Journal of Qualitative Theory of Differential Equations is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access. There are no charges and fees for publication, either.Additional details
Identifiers
- URL
- https://idus.us.es/handle//11441/148709
- URN
- urn:oai:idus.us.es:11441/148709