On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom

Jaume Llibre; Luis Fernando Mello

doi:https://doi.org/10.1016/j.geomphys.2011.12.017

On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom

Jaume Llibre, Luis Fernando Mello

Department of Mathematics

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

1 Citation (Scopus)

Abstract

We study periodic orbits of Hamiltonian differential systems with three degrees of freedom using the averaging theory. We have chosen the classical integrable Hamiltonian system with the Hooke potential and we study periodic orbits which bifurcate from the periodic orbits of the integrable system perturbed with a non-autonomous potential. © 2012 Elsevier B.V..

Original language	English
Pages (from-to)	1054-1063
Journal	Journal of Geometry and Physics
Volume	62
Issue number	5
DOIs	https://doi.org/10.1016/j.geomphys.2011.12.017
Publication status	Published - 1 May 2012

Keywords

Averaging theory
Hamiltonian system
Hooke potential
Periodic orbit

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title = "On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom",

abstract = "We study periodic orbits of Hamiltonian differential systems with three degrees of freedom using the averaging theory. We have chosen the classical integrable Hamiltonian system with the Hooke potential and we study periodic orbits which bifurcate from the periodic orbits of the integrable system perturbed with a non-autonomous potential. {\textcopyright} 2012 Elsevier B.V..",

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AB - We study periodic orbits of Hamiltonian differential systems with three degrees of freedom using the averaging theory. We have chosen the classical integrable Hamiltonian system with the Hooke potential and we study periodic orbits which bifurcate from the periodic orbits of the integrable system perturbed with a non-autonomous potential. © 2012 Elsevier B.V..

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KW - Hamiltonian system

KW - Hooke potential

KW - Periodic orbit

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