3 problems

Let $f$ be a $C^\infty$ surface diffeomorphism and let $b>0$. Let $N^{\mathrm{SRB}}_g(b)$ denote the number of SRB measures of $g$ with metric entropy larger than $b$. SRB-measure…

Viana's conjecture. If $f$ has only nonzero Lyapunov exponents at Lebesgue almost every point, then it admits some SRB measure.

Let $A\colon \mathbb T^3\to\mathbb T^3$ be the hyperbolic automorphism induced by the displayed integral matrix, and let $f$ be an analytic diffeomorphism in a sufficiently small n…