scholarly journals Relative entropy dimension of topological dynamical systems

2019 ◽  
Vol 39 (11) ◽  
pp. 6631-6642
Author(s):  
Xiaomin Zhou ◽  
Keyword(s):  
Dynamical Systems ◽  
Relative Entropy ◽  
Entropy Dimension ◽  
Topological Dynamical Systems

scholarly journals Generic points of shift-invariant measures in the countable symbolic space

2018 ◽  
Vol 166 (2) ◽  
pp. 381-413
Author(s):  
AI–HUA FAN ◽  
MING–TIAN LI ◽  
JI–HUA MA
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Invariant Measure ◽  
Gibbs Measure ◽  
Relative Entropy ◽  
Invariant Measures ◽  
Gibbs Measures ◽  
Symbolic Space ◽  
Entropy Dimension ◽  
Generic Points

AbstractWe are concerned with sets of generic points for shift-invariant measures in the countable symbolic space. We measure the sizes of the sets by the Billingsley-Hausdorff dimensions defined by Gibbs measures. It is shown that the dimension of such a set is given by a variational principle involving the convergence exponent of the Gibbs measure and the relative entropy dimension of the Gibbs measure with respect to the invariant measure. This variational principle is different from that of the case of finite symbols, where the convergent exponent is zero and is not involved. An application is given to a class of expanding interval dynamical systems.

scholarly journals Q-entropy for general topological dynamical systems

2019 ◽  
Vol 39 (4) ◽  
pp. 2059-2075 ◽  
Author(s):  
Yun Zhao ◽  
◽  
Wen-Chiao Cheng ◽  
Chih-Chang Ho ◽  
◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Topological Dynamical Systems

Almost topological dynamical systems

1979 ◽  
Vol 34 (1-2) ◽  
pp. 139-160 ◽  
Author(s):  
Manfred Denker ◽  
Michael Keane
Keyword(s):  
Dynamical Systems ◽  
Topological Dynamical Systems
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