scholarly journals Mean topological dimension for random bundle transformations

2017 ◽  
Vol 39 (4) ◽  
pp. 1020-1041
Author(s):  
XIANFENG MA ◽  
JUNQI YANG ◽  
ERCAI CHEN
Keyword(s):  
Dynamical Systems ◽  
Topological Entropy ◽  
Random Dynamical Systems ◽  
Boundary Property ◽  
Topological Dimension ◽  
The Mean

We introduce the mean topological dimension for random bundle transformations, and show that continuous bundle random dynamical systems with finite topological entropy or satisfying the small boundary property have zero mean topological dimensions.

scholarly journals METASTABILITY, LYAPUNOV EXPONENTS, ESCAPE RATES, AND TOPOLOGICAL ENTROPY IN RANDOM DYNAMICAL SYSTEMS

2013 ◽  
Vol 13 (04) ◽  
pp. 1350004 ◽  
Author(s):  
GARY FROYLAND ◽  
OGNJEN STANCEVIC
Keyword(s):  
Dynamical Systems ◽  
Finite Type ◽  
Topological Entropy ◽  
Lower Bounds ◽  
Random Systems ◽  
Random Dynamical Systems ◽  
Upper And Lower Bounds ◽  
Random System ◽  
Random Maps ◽  
Frobenius Operator

We explore the concept of metastability in random dynamical systems, focusing on connections between random Perron–Frobenius operator cocycles and escape rates of random maps, and on topological entropy of random shifts of finite type. The Lyapunov spectrum of the random Perron–Frobenius cocycle and the random adjacency matrix cocycle is used to decompose the random system into two disjoint random systems with rigorous upper and lower bounds on (i) the escape rate in the setting of random maps, and (ii) topological entropy in the setting of random shifts of finite type, respectively.

GROWTH IN TOPOLOGICAL COMPLEXITY AND VOLUME GROWTH FOR RANDOM DYNAMICAL SYSTEMS

2006 ◽  
Vol 06 (04) ◽  
pp. 459-471 ◽  
Author(s):  
YUJUN ZHU
Keyword(s):  
Dynamical Systems ◽  
Fundamental Group ◽  
Topological Entropy ◽  
Volume Growth ◽  
Point Of View ◽  
Random Dynamical Systems ◽  
Topological Complexity

In this paper, relations between topological entropy, volume growth and the growth in topological complexity from homotopical and homological point of view are discussed for random dynamical systems. It is shown that, under certain conditions, the volume growth, the growth in fundamental group and the growth in homological group are all bounded from above by the topological entropy.

VARIATIONAL PRINCIPLE FOR SUBADDITIVE SEQUENCE OF POTENTIALS IN BUNDLE RANDOM DYNAMICAL SYSTEMS

2009 ◽  
Vol 09 (02) ◽  
pp. 205-215 ◽  
Author(s):  
XIANFENG MA ◽  
ERCAI CHEN
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Multifractal Analysis ◽  
Weak Condition ◽  
Random Dynamical Systems ◽  
Topological Pressure ◽  
Set Up

The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in the study of multifractal analysis for random version of nonconformal dynamical systems.

Noise-induced unstable dimension variability and transition to chaos in random dynamical systems

2003 ◽  
Vol 67 (2) ◽  
Author(s):  
Ying-Cheng Lai ◽  
Zonghua Liu ◽  
Lora Billings ◽  
Ira B. Schwartz
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Transition To Chaos

scholarly journals On the Relation between Topological Entropy and Restoration Entropy

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 7 ◽  
Author(s):  
Christoph Kawan
Keyword(s):  
Dynamical Systems ◽  
State Estimation ◽  
Topological Entropy ◽  
Robust Estimation ◽  
Data Transmission ◽  
Communication Constraints ◽  
Dynamical Entropy

In the context of state estimation under communication constraints, several notions of dynamical entropy play a fundamental role, among them: topological entropy and restoration entropy. In this paper, we present a theorem that demonstrates that for most dynamical systems, restoration entropy strictly exceeds topological entropy. This implies that robust estimation policies in general require a higher rate of data transmission than non-robust ones. The proof of our theorem is quite short, but uses sophisticated tools from the theory of smooth dynamical systems.

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