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The Liapunov Center Theorem for a Class of Equivariant Hamiltonian Systems

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  • Jia Li
  • Yanling Shi

Abstract

We consider the existence of the periodic solutions in the neighbourhood of equilibria for ð ¶ âˆž equivariant Hamiltonian vector fields. If the equivariant symmetry 𠑆 acts antisymplectically and 𠑆 2 = ð ¼ , 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.

Suggested Citation

  • Jia Li & Yanling Shi, 2012. "The Liapunov Center Theorem for a Class of Equivariant Hamiltonian Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, January.
    • Handle: RePEc:hin:jnlaaa:530209
    DOI: 10.1155/2012/530209
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