Journal of Nonlinear Mathematical Physics

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Volume 21, Issue 3, June 2014, Pages 336 - 356

Periodic orbits associated to Hamiltonian functions of degree four

Authors
Dante Carrasco-Olivera*
Departamento de Matemática, Universidad del Bío- Bío Avda. Collao 1202, Concepcion, Chile,dcarrasc@ubiobio.cl
Marco Uribe†
Facultad de Ingeniería, Departamento de Matemática y Física Aplicadas, Universidad Católica de la Ssma. Concepción Casilla 297, Concepcion, Chile,muribe@ucsc.cl
Claudio Vidal‡
Departamento de Matemática, Universidad del Bío- Bío Avda. Collao 1202, Concepcion, Chile,clvidal@ubiobio.cl
*

The first author was partially supported by FONDECYT project 11121598, CONICYT (Chile), Grupo de Investigación Sistemas Dinámicos y Aplicaciones GI120708/EF, UBB (Chile) and Post-Doctorado Verano 2014, IMPA, Rio de Janeiro, Brazil.

†

The second author was partially supported by FONDECYT project 11080250, CONICYT (Chile), Post-Doctorado Verano 2014, IMPA, Rio de Janeiro, Brazil and Dirección de Investigación UCSC, Concepción (Chile).

‡

The third author was partially supported by FONDECYT project 1130644, CONICYT (Chile) and by Grupo de Investigación Sistemas Dinámicos y Aplicaciones GI120708/EF, UBB (Chile).

Received 24 January 2014, Accepted 25 March 2014, Available Online 6 January 2021.
DOI
10.1080/14029251.2014.936756How to use a DOI?
Keywords
Hamiltonian systems; Periodic orbits; Stability; Averaging theory
Abstract

We consider the Hamiltonian polynomial function H of degree fourth given by either H(x,y,px,py)=12(px2+py2)+12(x2+y2)+V3(x,y)+V4(x,y) , or H(x,y,px,py)=12(-px2+py2)+12(-x2+y2)+V3(x,y)+V4(x,y) , where V3 (x, y) and V4 (x, y) are homogeneous polynomials of degree three and four, respectively. Our main objective is to prove the existence and stability of periodic solutions associated to H using the classical averaging method.

Copyright
© 2014 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
21 - 3
Pages
336 - 356
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2014.936756How to use a DOI?
Copyright
© 2014 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Dante Carrasco-Olivera
AU  - Marco Uribe
AU  - Claudio Vidal
PY  - 2021
DA  - 2021/01/06
TI  - Periodic orbits associated to Hamiltonian functions of degree four
JO  - Journal of Nonlinear Mathematical Physics
SP  - 336
EP  - 356
VL  - 21
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2014.936756
DO  - 10.1080/14029251.2014.936756
ID  - Carrasco-Olivera2021
ER  -