20 citations · 42 across the 10 of their papers we have counts for
11 papers
Uniform quasi-multiplicativity of locally constant cocycles and applications
Reza Mohammadpour, Kiho Park
In this paper, we show that a locally constant cocycle is -quasi multiplicative under the irreducibility assumption. More precisely, we show that if $\mathcal{A}^t…
Pressure gaps, geometric potentials, and nonpositively curved manifolds
Dong Chen, Lien-Yung Kao, Kiho Park
In this paper, we derive a general pressure gap criterion for closed rank 1 manifolds whose singular sets are given by codimension 1 totally geodesic flat subtori. As an applicatio…
Construction and applications of proximal maps for typical cocycles
Kiho Park
For typical cocycles over subshifts of finite type, we show that for any given orbit segment, we can construct a periodic orbit such that it shadows the given orbit segment and tha…
Bernoulli property of subadditive equilibrium states
Benjamin Call, Kiho Park
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 abs…
Multifractal analysis of geodesic flows on surfaces without focal points
Kiho Park, Tianyu Wang
We study multifractal spectra of the geodesic flows on rank 1 surfaces without focal points. We compute the entropy of the level sets for the Lyapunov exponents and estimate its Ha…
Transfer operators and limit laws for typical cocycles
Kiho Park, Mark Piraino
We show that typical cocycles (in the sense of Bonatti and Viana) over irreducible subshifts of finite type obey several limit laws with respect to the unique equilibrium states fo…
The K-Property for Subadditive Equilibrium States
Benjamin Call, Kiho Park
By generalizing Ledrappier's criterion for the -property of equilibrium states, we extend the criterion to subadditive potentials. We apply this result to the singular value pot…
Properties of equilibrium states for geodesic flows over manifolds without focal points
Dong Chen, Lien-Yung Kao, Kiho Park
We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for Hölder potentials satisfying the pressure gap condition. In addition, we provid…
Thermodynamic formalism of -cocycles with canonical holonomies
Clark Butler, Kiho Park
We study singular value potentials of Hölder continuous -cocycles over hyperbolic systems whose canonical holonomies converge and are Hölder continuous. Such cocy…
Quasi-multiplicativity of typical cocycles
Kiho Park
We show that typical (in the sense of Bonatti-Viana) Hölder and fiber-bunched -valued cocycles over a subshift of finite type are uniformly quasi-multiplicative w…
Unique equilibrium states for geodesic flows over surfaces without focal points
Dong Chen, Lien-Yung Kao, Kiho Park
In this paper, we study dynamics of geodesic flows over closed surfaces of genus greater than or equal to 2 without focal points. Especially, we prove that there is a large class o…