Chaos and shadowing around a homoclinic tube

Yanguang (Charles) Li

Abstract and Applied Analysis, 2003, vol. 2003, 1-9

Abstract:

Let F be a C 3 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 ℝ n and the current work is done in a Banach space.

Date: 2003
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2003/681018.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2003/681018.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:681018

DOI: 10.1155/S1085337503304038

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().