On bifurcation of statistical properties of partially hyperbolic endomorphisms

Abstract

AbstractWe give an example of a path-wise connected open set of$C^{\infty }$partially hyperbolic endomorphisms on the$2$-torus, on which the (unique) Sinai–Ruelle–Bowen (SRB) measure exists for each system and varies smoothly depending on the system, while the sign of its central Lyapunov exponent changes.