Isochronicity for trivial quintic and septic planar polynomial hamiltonian systems

Francisco Braun; Jaume Llibre; Ana C. Mereu

doi:https://doi.org/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
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

Access to Document

https://doi.org/10.3934/dcds.2016029

https://ddd.uab.cat/record/169474

Cite this

@article{e2da0ca54cba40428bc90725a1c1daf2,

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.",

keywords = "Isochronous centers, Jacobian conjecture, Polynomial Hamiltonian systems",

author = "Francisco Braun and Jaume Llibre and Mereu, {Ana C.}",

year = "2016",

month = oct,

day = "1",

doi = "https://doi.org/10.3934/dcds.2016029",

language = "English",

volume = "36",

pages = "5245--5255",

number = "10",

}

TY - JOUR

T1 - Isochronicity for trivial quintic and septic planar polynomial hamiltonian systems

AU - Braun, Francisco

AU - Llibre, Jaume

AU - Mereu, Ana C.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - 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.

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

U2 - https://doi.org/10.3934/dcds.2016029

DO - https://doi.org/10.3934/dcds.2016029

M3 - Article

VL - 36

SP - 5245

EP - 5255

IS - 10

ER -

Isochronicity for trivial quintic and septic planar polynomial hamiltonian systems

Abstract

Keywords

Access to Document

Fingerprint

Cite this