scholarly journals Relative tail entropy for random bundle transformations

2017 ◽  
Vol 18 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Xianfeng Ma ◽  
Junqi Yang ◽  
Ercai Chen
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Random Dynamical Systems

We introduce the relative tail entropy to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail entropy is conserved by the principal extension.

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.

scholarly journals Subadditive Pre-Image Variational Principle for Bundle Random Dynamical Systems

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 309
Author(s):  
Xianfeng Ma ◽  
Zhongyue Wang ◽  
Hailin Tan
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Random Dynamical Systems ◽  
Topological Pressure ◽  
Image Measure ◽  
Measure Preserving Transformations

A central role in the variational principle of the measure preserving transformations is played by the topological pressure. We introduce subadditive pre-image topological pressure and pre-image measure-theoretic entropy properly for the random bundle transformations on a class of measurable subsets. On the basis of these notions, we are able to complete the subadditive pre-image variational principle under relatively weak conditions for the bundle random 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 A random dynamical systems perspective on stochastic resonance

Nonlinearity ◽  
2017 ◽  
Vol 30 (7) ◽  
pp. 2835-2853 ◽  
Author(s):  
Anna Maria Cherubini ◽  
Jeroen S W Lamb ◽  
Martin Rasmussen ◽  
Yuzuru Sato
Keyword(s):  
Dynamical Systems ◽  
Stochastic Resonance ◽  
Random Dynamical Systems ◽  
Systems Perspective
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