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Exponentially Small Splitting of Invariant Manifolds of Parabolic Points
Inmaculada Baldomá and Ernest Fontich, University of Barcelona, Spain
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Memoirs of the American Mathematical Society
2004; 83 pp; softcover
Volume: 167
ISBN-10: 0-8218-3445-2
ISBN-13: 978-0-8218-3445-9
List Price: US$60
Individual Members: US$36
Institutional Members: US$48
Order Code: MEMO/167/792
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We consider families of one and a half degrees of freedom Hamiltonians with high frequency periodic dependence on time, which are perturbations of an autonomous system.

We suppose that the origin is a parabolic fixed point with non-diagonalizable linear part and that the unperturbed system has a homoclinic connection associated to it. We provide a set of hypotheses under which the splitting is exponentially small and is given by the Poincaré-Melnikov function.

Readership

Graduate students and research mathematicians interested in dynamical systems and ergodic theory.

Table of Contents

  • Notation and main results
  • Analytic properties of the homoclinic orbit of the unperturbed system
  • Parameterization of local invariant manifolds
  • Flow box coordinates
  • The extension theorem
  • Splitting of separatrices
  • References
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