Symbolic Dynamics of Odd Discontinuous Bimodal Maps

On the abundance of $k$-fold semi-monotone minimal sets in bimodal circle maps

Inspired by a twist maps theorem of Mather we study recurrent invariant sets that are ordered like rigid rotation under the action of the lift of a bimodal circle map $g$ to the $k$-fold cover. For each irrational in the interior of the rotation set the collection of the $k$-fold ordered semi-Denjoy minimal sets with that rotation number contains a $(k-1)$-dimensional ball in the weak topology on their unique invariant measures. We also describe completely their periodic orbit analogs for rational rotation numbers. The main tool is a generalization of a construction of Hedlund and Morse which …

Symbolic Representations of Iterated Maps

This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general subshift over usually an uncountable alphabet. It is shown that at most the second order representation is enough for a continuous map. In particular, it is shown that the dynamics of one-dimensional continuous maps to a great extent can be transformed to the study of subshift structure of a general symbolic dynamics system. By introducing distillations, partial …

分段单调区间映射的阴影性质

The shadowing property for piecewise monotone interval maps

本文针对由传递分段单调区间映射（特别是β-变换）驱动的非连续动力系统，给出简短证明表明其不具有阴影性质，从而补充并推广了Chen和Portela的已有结果。