Chaos and shadowing around a homoclinic tube
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 resul...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503304038 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |