COMMON EXTENSIONS AND HYPERBOLIC FACTOR MAPS FOR CODED SYSTEMS

被引：9

作者：

FIEBIG, D ^{[1
]}

机构：

[1] UNIV HEIDELBERG,DEPT ANGEW MATH,D-69120 HEIDELBERG,GERMANY

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 1995年 / 15卷

关键词：

D O I：

10.1017/S014338570000849X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The classification of dynamical systems by the existence of certain common extensions has been carried out very successfully in the class of shifts of finite type ('finite equivalence', 'almost topological conjugacy'). We consider generalizations of these notions in the class of coded systems. Topological entropy is shown to be a complete invariant for the existence of a common coded entropy preserving extension. In contrast to the shift of finite type setting, this extension cannot be made bounded-to-1 in general. Common extensions with hyperbolic factor maps lead to a version of almost topological conjugacy for coded systems.

引用

页码：517 / 534

页数：18

共 11 条

[1]

Ashley J., Bounded-to-1 factors of an aperiodic shift of finite type are 1-to-1 almost everywhere also, Ergod. Th. & Dynam. Sys., 10, pp. 615-625, (1990)

[2]

Adler R., Marcus B., Topological entropy and equivalence of dynamical systems, Mem. Amer. Math. Soc., 219, (1979)

[3]

Blanchard F., Extensions à fibre constante, Ergod. Th. & Dynam. Sys., 11, pp. 7-17, (1991)

[4]

Blanchard F., Hansel G., Systèmes codés, Theoret. Comput. Sci., 44, pp. 17-49, (1986)

[5]

Bertrand-Mathis A., Specification and synchronisation

[6]

Denker M., Grillenberger C., Sigmund K., Ergodic Theory on Compact Spaces. Springer Lecture notes in Mathematics 527, (1976)

[7]

Fiebig D., Common closing extensions and finitary regular isomorphism for synchronized systems, Amer. Math. Soc. Conm. Symbolic Dynamics and its Application, 135, pp. 125-138, (1992)

[8]

Fiebig D., Fiebig U., Covers for coded systems, Amer. Math. Soc. Conm. Symbolic Dynamics and its Application, 135, pp. 139-180, (1992)

[9]

Grillenberger C., Constructions of strictly ergodic systems I. Given entropy, Z. Wahrscheinlichkeitstheorie.verw.Gebiete, 25, pp. 323-334, (1973)

[10]

Parry W., A finitary classification of topological Markov chains and sofic systems, Bull. London Math. Soc., 9, pp. 86-92, (1977)

← 1 2 →