SMOOTH MARKOV PARTITIONS AND TORAL AUTOMORPHISMS

被引：14

作者：

CAWLEY, E

机构：

[1] Mathematical Sciences Research Institute, Berkeley

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 1991年 / 11卷

关键词：

D O I：

10.1017/S0143385700006404

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the only hyperbolic toral automorphisms f for which there exist Markov partitions with piecewise smooth boundary are those for which a power f(k) is linearly covered by a direct product of automorphisms of the 2-torus. Only a finite number of shapes occur in a certain natural set of cross-sections of the partition boundary. The behavior of the stratified structure of a piecewise smooth boundary under the mapping forces these shapes to be self-similar. This, together with expanding properties of the mapping, means that a piecewise smooth partition is in fact piecewise linear. Orbits of affine disks in the boundary are used to construct a basis of 2-dimensional invariant toral subgroups, and then the product decomposition of a covering follows easily.

引用

页码：633 / 651

页数：19

共 9 条

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