Denominator bounds in Thompson-like groups and flows

Climenhaga-Thompson 判据的改进版本：局部极大集情形

An Improved Climenhaga-Thompson Criterion for Locally Maximal Sets

本文在弱非均匀条件下，改进 Climenhaga-Thompson 判据，证明了紧致局部极大不变集上连续流平衡态的存在唯一性。

Rational integrals of 2-dimensional geodesic flows: new examples

This paper is devoted to searching for Riemannian metrics on 2-surfaces whose geodesic flows admit a rational in momenta first integral with a linear numerator and denominator. The explicit examples of metrics and such integrals are constructed. Few superintegrable systems are found having both a polynomial and a rational integrals which are functionally independent of the Hamiltonian.

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 $λ$-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 Mañé diffeomorphisms and the Katok map. Our argument builds on the orbit decomposition theory of Climenhaga and Thompson.

The weighted Farey sequence and a sliding section for the horocycle flow

The Farey sequence is the sequence of all rational numbers in the real unit interval, stratified by increasing denominators. A classical result by Hall says that its normalized gap distribution is the same as the distribution of the random variable 1/(2 zeta(2) xy) on a certain unit triangle. In this paper we weight the denominators by an arbitrary piecewise-smooth continuous function, and we characterize the resulting gap distribution as that of a multiple of the above variable, defined on a certain unit pentagon. Our characterization refines previous results by Boca, Cobeli and Zaharescu, bu…

Salem型替换上悬浮流谱测度的连续模

Modulus of continuity for spectral measures of suspension flows over Salem type substitutions

本文研究Salem型替换生成的悬浮流谱测度，对域Q(α)中远离零点的点给出仅由绝对值、实共轭绝对值和分母三个参数决定的Hölder指数。

On Bowen's entropy inequality and almost specification for flows

We study the Bowen topological entropy of generic and irregular points for certain dynamical systems. We define the topological entropy of noncompact sets for flows, analogous to Bowen's definition. We show that this entropy coincides with the Bowen topological entropy of the time-1 map on any set. We also show a Bowen's inequality for flows; namely, that the metric entropy with respect to every invariant measure for a continuous flow is an upper bound for the topological entropy of the set of generic points with respect to the same measure, and the equality is always true if the measure is er…