Uniform subharmonic orbits for Sitnikov problem

Clark Robinson

doi:10.3934/dcdss.2008.1.647

Article Contents

2008, Volume 1, Issue 4: 647-652. Doi: 10.3934/dcdss.2008.1.647

This issue Previous Article A proof of Saari's conjecture for the three-body problem in $\R^d$ Next Article Reflections on the "Saari Conjecture" and several new ones

Uniform subharmonic orbits for Sitnikov problem

Clark Robinson^1,

1.
Department of Mathematics, Northwestern University, Evanston IL 60208

Received: March 2008

Revised: July 2008

Published: December 2008

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Abstract

We highlight the argument in Moser's monograph that the subharmonic periodic orbits for the Sitnikov problem exist uniformly for the eccentricity sufficiently small. We indicate how this relates to the uniformity of subharmonic periodic orbits for a forced Hamiltonian system of one degree of freedom with a symmetry.

Keywords:

Melnikov function,
Sitnikov problem.

Mathematics Subject Classification: 34C60, 70F07.

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