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Generic drift on Cantor sets of annuli. (English) Zbl 1034.70012
Chenciner, Alain (ed.) et al., Celestial mechanics. Dedicated to Donald Saari for his 60th birthday. Proceedings of an international conference, Northwestern Univ., Evanston, IL, USA, December 15–19, 1999. Providence, RI: AMS, American Mathematical Society (ISBN 0-8218-2902-5). Contemp. Math. 292, 163-171 (2002).
Summary: This note is devoted to studying the dynamics on an invariant Cantor set of annuli analogous to the invariant Cantor set of points of the horseshoe map. It is shown that generically, such a set contains orbits for which the action variable on the annulus “drifts”. Motivation comes from the problem of Arnold diffusion in Hamiltonian systems.
For the entire collection see [Zbl 0983.00061].

MSC:
70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
37N05 Dynamical systems in classical and celestial mechanics
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