Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems

Released on by Laurent Lazzarini
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  • Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems Book Detail

  • Author : Laurent Lazzarini
  • Release Date : 2019-02-21
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 122
  • ISBN 13 : 147043492X
  • File Size : 6,6 MB
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Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems by Laurent Lazzarini PDF Summary

Book Description: A wandering domain for a diffeomorphism of is an open connected set such that for all . The authors endow with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map of a Hamiltonian which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the “quantitative Hamiltonian perturbation theory” initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.

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Algebraic Geometry over C∞-Rings

Algebraic Geometry over C∞-Rings

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If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operatio