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- Title
Nilpotent bi-center in continuous piecewise Z2-equivariant cubic polynomial Hamiltonian systems.
- Authors
Chen, Ting; Li, Shimin; Llibre, Jaume
- 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.
- Subjects
POLYNOMIALS
- Publication
Nonlinear Dynamics, 2022, Vol 110, Issue 1, p705
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-022-07631-z