Research
My research interests include thermodynamic formalism, ergodic theory, and equilibrium states arising from geometric systems. I'm particularly interested in studying dynamical systems beyond uniform hyperbolicity.
Publications
Bernoulli Property of Subadditive Equilibrium States (with Kiho Park) - published in Mathematische Zeitschrift
We show that for certain subadditive equilibrium states, the K-property implies the Bernoulli property. We do this by showing that they satisfy a version of local product structure.
Unique Equilibrium States of Geodesic Flows on Flat Surfaces with Singularities (with Dave Constantine, Alena Erchenko, Noelle Sawyer, and Grace Work) - published in International Mathematics Research Notices
Given a flat surface with finitely many conical singularities of angle greater than 2pi, we establish uniqueness of equilibrium states for a wide class of potentials, following the technique in the work of Burns, Climenhaga, Fisher, and Thompson. We also show that these equilibrium states have the K-property.
The K-Property for Some Unique Equilibrium States in Flows and Homeomorphisms - published in Ergodic Theory and Dynamical Systems
We establish general criteria for proving the K-property, building on the Climenhaga-Thompson machinery. We introduce one-sided lambda decompositions, and apply the criteria to both Mañé diffeomorphisms and the Katok map
The K-Property for Subadditive Equilibrium States (with Kiho Park) - published in Dynamical Systems: an International Journal
We generalize Ledrappier's criterion for the K-property to subadditive equilibrium states, and use it to show that totally ergodic subadditive equilibrium states with bounded distortion and quasi-multiplicativity have the K-property. We apply this to subadditive potentials arising from certain classes of matrix cocycles.
Equilibrium States for Self-Products of Flows and the Mixing Properties of Rank 1 Geodesic Flows (with Daniel Thompson) - published in Journal of the London Mathematical Society
Given a closed rank one manifold, Burns, Climenhaga, Fisher, and Thompson established uniqueness of equilibrium states for a wide class of potentials. We show that these equilibrium states have the K-property, and further, that the Bowen-Margulis measure is Bernoulli.