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.
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).