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. |
Rights: |
Tots els drets reservats. |
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
Available from: 2024-09-30
Postprint
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Record created 2024-02-27, last modified 2024-05-06