Measure Expansivity and Specification for Pointwise Dynamics

Pointwise dynamics under Orbital Convergence

We obtain sufficient conditions under which the limit of a sequence of functions exhibits a particular dynamical behaviour at a point like expansivity, shadowing, mixing, sensitivity and transitivity. We provide examples to show that the set of all expansive, positively expansive and sensitive points are neither open nor closed in general. We also observe that the set of all transitive and mixing points are closed but not open in general. We give examples to show that properties like expansivity, sensitivity, shadowing, transitivity and mixing at a point need not be preserved under uniform con…

具有扩张性和规范性的非紧系统的热力学形式

Thermodynamic formalism for non-compact systems with expansivity and specification

针对完备可分度量空间上的连续流，利用规范性质发展了平衡态理论，引入强正递归概念证明平衡态的存在唯一性，应用于无挤压负曲率流形和CAT(-1)空间上的测地流。

Intrinsic ergodicity via obstruction entropies

Bowen showed that a continuous expansive map with specification has a unique measure of maximal entropy. We show that the conclusion remains true under weaker non-uniform versions of these hypotheses. To this end, we introduce the notions of obstructions to expansivity and specification, and show that if the entropy of such obstructions is smaller than the topological entropy of the map, then there is a unique measure of maximal entropy.

单纯形动力学中的全测历史行为与涌现

Full-measure historic behavior and emergence in simplex dynamics

本文提出一种有限维边界驻留机制，使单纯形映射的非固定轨道产生非收敛历史行为，且历史集具全测度，并给出经验测度累积集及多项式涌现阶。