Topological r-entropy and Measure Theoretic r-entropy of Flows

被引：0

作者：

Yong JI ^{[1
]}

Yun Ping WANG ^{[2
,3
]}

机构：

[1] Department of Mathematics, Ningbo University

[2] School of Science, Ningbo University of Technology

[3] School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University

来源：

Acta Mathematica Sinica,English Series | 2022年 / 04期

关键词：

D O I：

暂无

中图分类号：

O174.12 [测度论]; O177.99 [其他];

学科分类号：

摘要：

The topological r-entropy and measure theoretic r-entropy of a flow are studied. For a flow(X, φ), it is shown that topological(measure theoretic) r-entropy is equal to the topological(measure theoretic) entropy of the time one map φ1 as r decreases to zero. The Brin–Katok’s entropy formula for r-entropy is also established.

引用

页码：761 / 769

页数：9

共 50 条

[21] Some Notes on Topological and Measure-Theoretic Entropy
Tao Wang
Qualitative Theory of Dynamical Systems, 2021, 20
[22] AN ESTIMATE FOR THE MEASURE THEORETIC ENTROPY OF GEODESIC-FLOWS
BALLMANN, W
WOJTKOWSKI, MP
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1989, 9 : 271 - 279
[23] Topological unified (r, s)-entropy
Kazemi, R.
Miri, M. R.
Borzadaran, G. R. Mohtashami
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2020, 541
[24] Measure-theoretic and topological entropy of operators on function spaces
Downarowicz, T
Frej, B
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 : 455 - 481
[25] On the measure-theoretic entropy and topological pressure of free semigroup actions
Lin, Xiaogang
Ma, Dongkui
Wang, Yupan
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2018, 38 : 686 - 716
[26] Topological entropy of autonomous flows
Badii, R
PHYSICAL REVIEW E, 1996, 54 (05) : R4496 - R4499
[27] On the topological entropy of geodesic flows
Mane, R
JOURNAL OF DIFFERENTIAL GEOMETRY, 1997, 45 (01) : 74 - 93
[28] Topological entropy of stable flows
Thomas, RF
THIRD INTERNATIONAL CONFERENCE ON NONLINEAR PROBLEMS IN AVIATION AND AEROSPACE, VOLS 1 AND 2, PROCEEDINGS, 2002, : 639 - 644
[29] Topological entropy of autonomous flows
Phys Rev E., 5 (R4496):
[30] A generalized complexity measure based on Rényi entropy
Pablo Sánchez-Moreno
Juan Carlos Angulo
Jesus S. Dehesa
The European Physical Journal D, 2014, 68

← 1 2 3 4 5 →