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Arnold Diffusion in A Priori Chaotic Symplectic Maps

Abstract

We assume that a symplectic real-analytic map has an invariant normally hyperbolic cylinder and an associated transverse homoclinic cylinder. We prove that generically in the real-analytic category the boundaries of the invariant cylinder are connected by trajectories of the map.

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Correspondence to Dmitry Turaev.

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Communicated by J. Marklof

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Gelfreich, V., Turaev, D. Arnold Diffusion in A Priori Chaotic Symplectic Maps. Commun. Math. Phys. 353, 507–547 (2017). https://doi.org/10.1007/s00220-017-2867-0

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