Isochronicity for trivial quintic and septic planar polynomial hamiltonian systems

Francisco Braun; Jaume Llibre; Ana C. Mereu

doi:10.3934/dcds.2016029

Isochronicity for trivial quintic and septic planar polynomial hamiltonian systems

Francisco Braun, Jaume Llibre, Ana C. Mereu

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

In this paper we completely characterize trivial polynomial Hamiltonian isochronous centers of degrees 5 and 7. Precisely, we provide simple formulas, up to linear change of coordinates, for the Hamiltonians of the form H = (f21 + f22)/2, where f = (f1, f2) : R2 → R2 is a polynomial map with det Df = 1, f(0, 0) = (0; 0) and the degree of f is 3 or 4.

Original language	English
Pages (from-to)	5245-5255
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	36
Issue number	10
DOIs	https://doi.org/10.3934/dcds.2016029
Publication status	Published - 1 Oct 2016

Keywords

Isochronous centers
Jacobian conjecture
Polynomial Hamiltonian systems

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title = "Isochronicity for trivial quintic and septic planar polynomial hamiltonian systems",

abstract = "In this paper we completely characterize trivial polynomial Hamiltonian isochronous centers of degrees 5 and 7. Precisely, we provide simple formulas, up to linear change of coordinates, for the Hamiltonians of the form H = (f21 + f22)/2, where f = (f1, f2) : R2 → R2 is a polynomial map with det Df = 1, f(0, 0) = (0; 0) and the degree of f is 3 or 4.",

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AB - In this paper we completely characterize trivial polynomial Hamiltonian isochronous centers of degrees 5 and 7. Precisely, we provide simple formulas, up to linear change of coordinates, for the Hamiltonians of the form H = (f21 + f22)/2, where f = (f1, f2) : R2 → R2 is a polynomial map with det Df = 1, f(0, 0) = (0; 0) and the degree of f is 3 or 4.

KW - Isochronous centers

KW - Jacobian conjecture

KW - Polynomial Hamiltonian systems

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DO - 10.3934/dcds.2016029

M3 - Article

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