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Codimension one generic homoclinic classes with interior


We study C 1-generic diffeomorphisms with a homoclinic class with non empty interior and in particular those admitting a codimension one dominated splitting. We prove that if in the finest dominated splitting the extreme subbundles are one dimensional then the diffeomorphism is partially hyperbolic and from this we deduce that the diffeomorphism is transitive.

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Correspondence to Rafael Potrie.

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Potrie, R., Sambarino, M. Codimension one generic homoclinic classes with interior. Bull Braz Math Soc, New Series 41, 125–138 (2010).

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  • Dominated splitting
  • C1 generic dynamics
  • homoclinic classes

Mathematical subject classification

  • 37D30
  • 37C20
  • 37C70