Abstract and Applied Analysis

The Liapunov Center Theorem for a Class of Equivariant Hamiltonian Systems

Jia Li and Yanling Shi

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Abstract

We consider the existence of the periodic solutions in the neighbourhood of equilibria for C equivariant Hamiltonian vector fields. If the equivariant symmetry S acts antisymplectically and S 2 = I , we prove that generically purely imaginary eigenvalues are doubly degenerate and the equilibrium is contained in a local two-dimensional flow-invariant manifold, consisting of a one-parameter family of symmetric periodic solutions and two two-dimensional flow-invariant manifolds each containing a one-parameter family of nonsymmetric periodic solutions. The result is a version of Liapunov Center theorem for a class of equivariant Hamiltonian systems.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 530209, 12 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495630

Digital Object Identifier
doi:10.1155/2012/530209

Mathematical Reviews number (MathSciNet)
MR2872320

Zentralblatt MATH identifier
1239.34049

Citation

Li, Jia; Shi, Yanling. The Liapunov Center Theorem for a Class of Equivariant Hamiltonian Systems. Abstr. Appl. Anal. 2012 (2012), Article ID 530209, 12 pages. doi:10.1155/2012/530209. https://projecteuclid.org/euclid.aaa/1355495630


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