10 problems

Let $M$ be a compact Riemannian manifold and let $f:M\rightarrow M$ be a $C^{2}$ local diffeomorphism. A transfer operator associated to a complex continuous potential…

Let $S$ be a compact surface, let $f\in \operatorname{Diff}^{1}(S)$ be a diffeomorphism, and let the potential be Holder continuous. A phase transition is a failure of analyticity…

Let $f:M\rightarrow M$ be a $C^{2}$ local diffeomorphism on a Riemannian manifold $M$. For a potential $\phi$, define the transfer operator by … A suitable Banach space may consist…

Let $(\Sigma,\sigma)$ be a finite entropy countable Markov shift, let $\rho$ be a totally bounded metric on its vertex set, and let $d$ be the corresponding metric on $\Sigma$. Wri…

Let $\Upsilon$ be the space of polygonal paths equipped with the push-forward a priori probability measure $p$, let $f$ be the potential … where $J(n)\geq 0$ tends to zero sufficie…

Let $(M,g)$ be a pinched negatively curved manifold. Let $(\mu_n)_n$ be a sequence of invariant probability measures converging vaguely to $\mu$, and let $F\in C_b(T^1M)$ be a unif…

Let $(A_1,\ldots,A_N)\in GL_d(\mathbb{R})$ and let $s\in(0,d)\smallsetminus\mathbb{Z}$. For a tuple of matrices, let $\varphi^s$ denote Falconer's singular value function, and call…

Let $N(\Omega):=N_{P(h)}(\Omega)$ be the resonance counting function, and let $\mathcal P_E(s)$ be the topological pressure. Resonance concentration conjecture. For every…

Let $N(\Omega):=N_{P(h)}(\Omega)$ be the resonance counting function, and let $\mathcal P_E(s)$ denote the topological pressure from the source. Pressure threshold conjecture. For…

Let $(X,Y,\pi)$ be a factor triple, let $\nu$ be a fully supported ergodic measure on $Y$, and let $c_\pi$ denote the class degree of the factor map. For a function…