Chaos and shadowing around a homoclinic tube

Yanguang (Charles) Li

Abstract and Applied Analysis, 2003, vol. 2003, issue 16, 923-931

Abstract: Let F be a C3 diffeomorphism on a Banach space B. F has a homoclinic tube asymptotic to an invariant manifold. Around the homoclinic tube, Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. This work removes an uncheckable condition of Silnikov (1968). Also, the result of Silnikov does not imply Bernoulli shift dynamics of a single map, but rather only provides a labeling of all invariant tubes around the homoclinic tube. The work of Silnikov was done in ℝn and the current work is done in a Banach space.

Date: 2003
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https://doi.org/10.1155/S1085337503304038

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