Coding and entropy for piecewise continuous piecewise monotone transformations

被引：2

作者：

Kopf, C ^{[1
]}

机构：

[1] Univ Innsbruck, Dept Math, A-6020 Innsbruck, Austria

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 61卷 / 1-2期

关键词：

piecewise continuous piecewise monotone transformations; topological entropy; symbolic dynamics;

D O I：

10.1016/j.na.2003.07.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use ideas of symbolic dynamics to define the topological entropy It (S) for a piecewise continuous piecewise monotone interval map S by counting the n-addresses of S with respect to a suitable system of pairwise disjoint open intervals. It turns out that this definition yields the same value as Bowen's definition using (n, epsilon)-separated and (n, epsilon)-spanning sets. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：269 / 275

页数：7

共 50 条

[1] MEASURES WITH MAXIMAL ENTROPY FOR PIECEWISE MONOTONE TRANSFORMATIONS OF AN INTERVAL
SIMONOV, AA
[J]. RUSSIAN MATHEMATICAL SURVEYS, 1980, 35 (05) : 273 - 274
[2] Symbol sequences and entropy for piecewise monotone transformations with discontinuities
Kopf, C
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2000, 6 (02): : 299 - 304
[3] ENTROPY OF PIECEWISE MONOTONE MAPPINGS
MISIUREWICZ, M
SZLENK, W
[J]. STUDIA MATHEMATICA, 1980, 67 (01) : 45 - 63
[4] On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Krzysztof Ciepliński
Marek Cezary Zdun
[J]. Fixed Point Theory and Applications, 2009
[5] On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Cieplinski, Krzysztof
Zdun, Marek Cezary
[J]. FIXED POINT THEORY AND APPLICATIONS, 2009,
[6] Strict inequalities for the entropy of transitive piecewise monotone maps
Misiurewicz, M
Raith, P
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2005, 13 (02): : 451 - 468
[7] ZETA-FUNCTIONS AND TRANSFER OPERATORS FOR PIECEWISE MONOTONE TRANSFORMATIONS
BALADI, V
KELLER, G
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 127 (03) : 459 - 477
[8] INVESTIGATION OF PIECEWISE MONOTONE TRANSFORMATIONS OF AN INTERVAL BY METHODS OF SYMBOLIC DYNAMICS
SIMONOV, AA
[J]. DOKLADY AKADEMII NAUK SSSR, 1978, 238 (05): : 1063 - 1066
[9] REALIZATIONS OF GROUPS OF PIECEWISE CONTINUOUS TRANSFORMATIONS OF THE CIRCLE
Cornulier, Yves
[J]. JOURNAL OF MODERN DYNAMICS, 2020, 16 : 59 - 80
[10] Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval
Kolyada, S
Misiurewicz, M
Snoha, L
[J]. FUNDAMENTA MATHEMATICAE, 1999, 160 (02) : 161 - 181

← 1 2 3 4 5 →