A new measure of instability and topological entropy of area-preserving twist diffeomorphisms

  title={A new measure of instability and topological entropy of area-preserving twist diffeomorphisms},
  author={Sini{\vs}a Slijep{\vc}evi{\'c}},
We introduce a new measure of instability of area-preserving twist diffeomorphisms, which generalizes the notions of angle of splitting of separatrices, and flux through a gap of a Cantori. As an example of application, we establish a sharp >0 lower bound on the topological entropy in a neighbourhood of a hyperbolic, unique action-minimizing fixed point, assuming only no topological obstruction to diffusion, i.e. no homotopically non-trivial invariant circle consisting of orbits with the… 

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Monotone recurrence relations, their Birkhoff orbits and topological entropy

  • S. Angenent
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1990
Abstract A generalization of the class of monotone twistmaps to maps of s1 × RN is proposed. The existence of Birkhoff orbits is studied, and a criterion for positive topological entropy is given.

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