12 problems

Let $f$ be a smooth map and suppose that all its Lyapunov exponents are nonzero at Lebesgue almost every point. Viana's conjecture. The map $f$ admits an SRB measure. This conjectu…

Let $\mu_\eps$ be the invariant measure of a noisy dynamical system and let $\mu_{\mathrm{SRB}}$ be the corresponding SRB measure of the deterministic system. In uniformly hyperbol…

Let $f$ be an analytic surface diffeomorphism with dominated splitting, let ${\Cal N}$ denote the relevant set of periodic points, let $\lambda_F$ be the associated quantity on per…

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…

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…

Let $f:M\to M$ be an endomorphism, and let an SRB measure mean an invariant measure whose unstable conditional parts are absolutely continuous with respect to Lebesgue measure. The…

Let $f$ be a $C^2$ regular map (local diffeomorphism) on a compact closed Riemannian manifold. An SRB measure is an invariant measure whose unstable conditional parts are absolutel…

Generic slow-recurrence conjecture. This conclusion should also hold when $t_0$ satisfies a more generic slow recurrence condition, such as polynomial recurrence, possibly after in…

Slow-recurrence conjecture. Corollary should hold for every Collet–Eckmann parameter $t_0$ with sufficiently slow recurrence.

Slow-recurrence conjecture. Theorem should hold for $\Delta$ equal to the set of all sufficiently slowly recurrent parameters, including parameters with polynomial recurrence of ex…

Let $f$ be a $C^1$ expanding map on a compact manifold of arbitrary dimension. The results proved in this paper for $C^1$ expanding maps of the circle should also hold for $f$ in a…

Let $\Lambda\subset\mathbb{R}^d$ be an attractor supporting a Sinai–Ruelle–Bowen measure $\nu$ and admitting a local product structure. Write the local measure as…