On bifurcation of statistical properties of partially hyperbolic endomorphisms

Abstract

We give an example of a path-wise connected open set of $C^{\infty }$ partially hyperbolic endomorphisms on the $2$-torus, on which the SRB measure exists for each system and varies smoothly depending on the system, while the sign of its central Lyapunov exponent does change.

10 pages, 3 figures