Generation of homoclinic tangencies by $C^1$-perturbations.
GOURMELON, Nicolas
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Institut de Mathématiques de Bordeaux [IMB]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Institut de Mathématiques de Bordeaux [IMB]
GOURMELON, Nicolas
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Discrete and Continuous Dynamical Systems - Series A. 2010, vol. 26, n° 1, p. 1-42
American Institute of Mathematical Sciences
English Abstract
Given a [C^1] -diffeomorphism [f] of a compact manifold, we show that if the stable/unstable dominated splitting along a saddle is weak enough, then there is a small [C^1] -perturbation that preserves the orbit of the ...Read more >
Given a [C^1] -diffeomorphism [f] of a compact manifold, we show that if the stable/unstable dominated splitting along a saddle is weak enough, then there is a small [C^1] -perturbation that preserves the orbit of the saddle and that generates a homoclinic tangency related to it. Moreover, we show that the perturbation can be performed preserving a homoclinic relation to another saddle. We derive some consequences on homoclinic classes. In particular, if the homoclinic class of a saddle [P] has no dominated splitting of same index as [P] , then a [C^1] -perturbation generates a homoclinic tangency related to [P] .Read less <
English Keywords
Dominated splitting
homoclinic tangency
bifurcation
homoclinic class.
homoclinic class
Origin
Hal imported