arXiv subjects

Benjamin Call

Publications and source records attributed to Benjamin Call.

6 recordsLinked to original sources

arXiv2024

Local product structure for equilibrium states of geodesic flows and applications

Let $S$ be a compact surface of genus $\geq 2$ equipped with a metric that is flat everywhere except at finitely many cone points with angles greater than $2\pi$. We examine the geodesic flow on $S$ and prove local product structure for a wide class of equilibrium states. Using this, we establish the Bernoulli property for these systems. We also establish local product structure for a similar class of equilibrium states for geodesic flows on rank 1, nonpositively curved manifolds.

math.DS↗

arXiv2021

Bernoulli property of subadditive equilibrium states

Under mild assumptions, we show that the unique subadditive equilibrium states for fiber-bunched cocycles are Bernoulli. We achieve this by showing these equilibrium states are absolutely continuous with respect to a product measure, and then using the Kolmogorov property of these measures.

math.DS↗

arXiv2021

Unique equilibrium states for geodesic flows on flat surfaces with singularities

Consider a compact surface of genus $\geq 2$ equipped with a metric that is flat everywhere except at finitely many cone points with angles greater than $2\pi$. Following the technique in the work of Burns, Climenhaga, Fisher, and Thompson, we prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not support the full pressure. Moreover, we show that the pressure gap holds for any potential which is locally constant on a neighborhood of the singular set. Finally, we establish that the corresponding equilibrium states have the $K$-property, and closed regular geodesics equidistribute.

math.DS↗

arXiv2020

The K-Property for Some Unique Equilibrium States in Flows and Homeomorphisms

We set out some general criteria to prove the K-property, refining the assumptions used in arXiv:1906.09315 for the flow case, and introducing the analogous discrete-time result. We also introduce one-sided $\lambda$-decompositions, as well as multiple techniques for checking the pressure gap required to show the K-property. We apply our results to the family of Ma\~n\'e diffeomorphisms and the Katok map. Our argument builds on the orbit decomposition theory of Climenhaga and Thompson.

math.DS↗

arXiv2020

The K-Property for Subadditive Equilibrium States

By generalizing Ledrappier's criterion for the $K$-property of equilibrium states, we extend the criterion to subadditive potentials. We apply this result to the singular value potentials of matrix cocycles, and show that equilibrium states of large classes of singular value potentials have the $K$-property.

math.DS↗

arXiv2019

Equilibrium states for self-products of flows and the mixing properties of rank 1 geodesic flows

Equilibrium states for geodesic flows over closed rank 1 manifolds were studied recently by Burns, Climenhaga, Fisher and Thompson. For sufficiently regular potentials, it was shown that if the singular set does not carry full pressure then the equilibrium state is unique. The main result of this paper is that these equilibrium states have the Kolmogorov property. In particular, these measures are mixing of all orders and have positive entropy. For the Bowen-Margulis measure, we go further and obtain the Bernoulli property from the K-property using classic arguments from Ornstein theory. Our argument for the K-property is based on an idea due to Ledrappier. We prove uniqueness of equilibrium states on the product of the system with itself. To carry this out, we develop techniques for uniqueness of equilibrium states which apply in the presence of the 2-dimensional center direction which appears for a product of flows. This is a key technical challenge of this paper.

math.DS↗