Openess of the set of non-uniform hyperbolic diffeomorphisms.
It has been proved by Bochi that the set of non-uniform hyperbolic diffemorphisms is not C1 open among partially hyperbolic symplectic diffemorphisms. More recently, with C. Liang and J. Yang, we obtained the Cr openess of the set of non-uniform hyperbolic diffeomorphisms in a subset of partially hyperbolic symplectic diffeomorphisms with 2-dimensional center bundle for any r 2. In this talk, we are going to discuss the intermediary case between the C1 and C2 topology. This is a joint work with C. Liang and J. Yang..