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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2010

Generation of homoclinic tangencies by $C^1$-perturbations.

Résumé

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] .

Dates et versions

hal-00489042 , version 1 (03-06-2010)

Identifiants

Citer

Nicolas Gourmelon. Generation of homoclinic tangencies by $C^1$-perturbations.. Discrete and Continuous Dynamical Systems - Series A, 2010, 26 (1), pp.1-42. ⟨10.3934/dcds.2010.26.1⟩. ⟨hal-00489042⟩
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