Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms

• 成果类型: Article
• 署名作者: Crovisier, Sylvain; Pujals, Enrique R.
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Instituto Nacional de Matematica Pura e Aplicada (IMPA)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0553-9
• 发表日期: 2015
• 页码: 385-517
• 关键词: dynamical-systems; STABILITY; tangencies; dimension; density; cycles

摘要

We prove that any diffeomorphism of a compact manifold can be approximated in the topology by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (has a finite number of transitive hyperbolic attractors with open and dense basin of attraction).