We start by stating a version of the Perronâ€“Frobenius theorem. Let A be a d Ã— d stochastic matrix, where here we use this to mean that the entries of A are non-negative, and every column sums to 1:â€¦ (More)

Using an approach due to Bowen, Franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property. We show that this conclusionâ€¦ (More)

It is well-known that for expansive maps and continuous potential functions, the specification property (for the map) and the Bowen property (for the potential) together imply the existence of aâ€¦ (More)

We give sufficient conditions for a shift space (Î£, Ïƒ) to be intrinsically ergodic, along with sufficient conditions for every subshift factor of Î£ to be intrinsically ergodic. As an application, weâ€¦ (More)

Multifractal analysis studies level sets of asymptotically defined quantities in a topological dynamical system. We consider the topological pressure function on such level sets, relating it both toâ€¦ (More)

We show that a shift space on a finite alphabet with a non-uniform specification property can be modeled by a strongly positive recurrent countable-state Markov shift to which every equilibrium stateâ€¦ (More)

We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potentials. In particular, we characterize the SRB measureâ€¦ (More)

Most results in multifractal analysis are obtained using either a thermodynamic approach based on existence and uniqueness of equilibrium states or a saturation approach based on some version of theâ€¦ (More)

We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This hasâ€¦ (More)