Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)

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

DOI: 10.3934/dcdsb.2019259

Postprint 26 p, 577.1 KB

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