Nilpotent Bicenters in Continuous Piecewise Z2 -Equivariant Cubic Polynomial Hamiltonian Vector Fields : Cusp-Cusp Type
Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2023
Abstract:	In this paper, we study the global dynamics for a class of continuous piecewise Z2-equivariant cubic Hamiltonian vector fields with nilpotent bicenters at (±1, 0). We consider these polynomial vector fields with a challenging case where the bicenters (±1, 0) come from the combination of two nilpotent cusps separated by y = 0. We call it a cusp-cusp type. We use the Poincare compactification, the blow-up theory, the index theory and the theory of discriminant sequence for determining the number of distinct or negative real roots of a polynomial, to classify the global phase portraits of these vector fields in the Poincare disc.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Nilpotent ; Bicenters ; Hamiltonian ; Phase portrait
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 12 (September 2023) , art. 2350138, ISSN 1793-6551

DOI: 10.1142/S0218127423501389

Postprint 36 p, 5.6 MB

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