Subcontinua of the closure of the unstable manifold at a homoclinic tangency

Citation
M. Barge et B. Diamond, Subcontinua of the closure of the unstable manifold at a homoclinic tangency, ERGOD TH DY, 19, 1999, pp. 289-307
Citations number
14
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
01433857 → ACNP
Volume
19
Year of publication
1999
Part
2
Pages
289 - 307
Database
ISI
SICI code
0143-3857(199904)19:<289:SOTCOT>2.0.ZU;2-C
Abstract
Suppose that F is a C-infinity diffeomorphism of the plane with hyperbolic fixed point p for which a branch of the unstable manifold, W-+(u)(p), has a same-sided quadratic tangency with the stable manifold, W-s(p). If the eig envalues of DF at p satisfy a non-resonance condition, each nonempty open s et of cl(W-+(u)(p)) contains a copy of any continuum that can be written as the inverse limit space of a sequence of unimodal bonding maps.