Chaos and shadowing around a homoclinic tube
Li, Yanguang (Charles)
Abstr. Appl. Anal., Tome 2003 (2003) no. 7, p. 923-931 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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 ${\mathbb R}^n$ and the current work is done in a Banach space.
Publié le : 2003-09-07
Classification:  35Bxx 
@article{1063629069,
     author = {Li, Yanguang (Charles)},
     title = {Chaos and shadowing around a homoclinic tube},
     journal = {Abstr. Appl. Anal.},
     volume = {2003},
     number = {7},
     year = {2003},
     pages = { 923-931},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1063629069}
}

Li, Yanguang (Charles). Chaos and shadowing around a homoclinic tube. Abstr. Appl. Anal., Tome 2003 (2003) no. 7, pp.  923-931. http://gdmltest.u-ga.fr/item/1063629069/