Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in $\mathbb {R}^4$

Released on by Naiara V. de Paulo
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  • Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in $\mathbb {R}^4$ Book Detail

  • Author : Naiara V. de Paulo
  • Release Date : 2018-03-19
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 118
  • ISBN 13 : 1470428016
  • File Size : 77,77 MB
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Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in $\mathbb {R}^4$ by Naiara V. de Paulo PDF Summary

Book Description: In this article the authors study Hamiltonian flows associated to smooth functions R R restricted to energy levels close to critical levels. They assume the existence of a saddle-center equilibrium point in the zero energy level . The Hamiltonian function near is assumed to satisfy Moser's normal form and is assumed to lie in a strictly convex singular subset of . Then for all small, the energy level contains a subset near , diffeomorphic to the closed -ball, which admits a system of transversal sections , called a foliation. is a singular foliation of and contains two periodic orbits and as binding orbits. is the Lyapunoff orbit lying in the center manifold of , has Conley-Zehnder index and spans two rigid planes in . has Conley-Zehnder index and spans a one parameter family of planes in . A rigid cylinder connecting to completes . All regular leaves are transverse to the Hamiltonian vector field. The existence of a homoclinic orbit to in follows from this foliation.

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