Home > Articles > Published articles > Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem |
Date: | 2020 |
Abstract: | We present a systematic methodology to determine and locate analytically isolated periodic points of discrete and continuous dynamical systems with algebraic nature. We apply this method to a wide range of examples, including a one-parameter family of counterexamples to the discrete Markus-Yamabe conjecture (La Salle conjecture); the study of the low periods of a Lotka-Volterra-type map; the existence of three limit cycles for a piecewise linear planar vector field; a new counterexample of Kouchnirenko conjecture; and an alternative proof of the existence of a class of symmetric central configuration of the (1 + 4)-body problem. |
Grants: | Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad DPI2016-77407-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-388 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Poincaré-Miranda theorem ; Periodic orbits ; Lotka-Volterra maps ; Thue-Morse maps ; Discrete Markus-Yamabe conjecture ; Kouchnirenko's conjecture ; Limit cycles ; Planar piecewise linear systems ; Central configurations |
Published in: | Discrete and continuous dynamical systems. Series B, Vol. 25, Issue 2 (February 2020) , p. 651-670, ISSN 1553-524X |
Postprint 26 p, 577.1 KB |