Nilpotent bi-center in continuous piecewise Z2-equivariant cubic polynomial Hamiltonian systems
Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics)
Li, Shimin (Guangdong University of Finance and Economics. School of Statistics and Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2022
Abstract:	One of the classical and difficult problems in the theory of planar differential systems is to classify their centers. Here we classify the global phase portraits in the Poincaré disk of the class continuous piecewise differential systems separated by one straight line and formed by two cubic Hamiltonian systems with nilpotent bi-center at (± 1, 0). The main tools for proving our results are the Poincaré compactification, the index theory, and the theory of sign lists for determining the exact number of real roots or negative real roots of a real polynomial in one variable.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Nilpotent ; Bi-center ; Hamiltonian ; Phase portrait
Published in:	Nonlinear Dynamics, Vol. 110, Issue 1 (September 2022) , p. 705-721, ISSN 1573-269X

DOI: 10.1007/s11071-022-07631-z

Postprint 18 p, 887.5 KB

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