Homoclinic points of symplectic partially hyperbolic systems with 2D centre

Abstract

We consider a generic symplectic partially hyperbolic diffeomorphism close to direct/skew products of symplectic Anosov diffeomorphisms with area-preserving diffeomorphisms and prove that every hyperbolic periodic point has transverse homoclinic points.

Keywords:

• Generic properties
• hyperbolic periodic point
• homoclinic points
• partial hyperbolicity
• centre foliation

2000 Mathematics Subject Classifications:

• 37C29
• 37C20
• 37D30

Acknowledgments

The author express his sincere gratitude to the anonymous referee for his/her invaluable comments, which help him to improve the presentation of the paper significantly.

Disclosure statement

No potential conflict of interest was reported by the author(s).