A Multiplicative Ergodic Theorem and Nonpositively Curved Spaces

1999 ◽  
Vol 208 (1) ◽  
pp. 107-123 ◽  
Author(s):  
Anders Karlsson ◽  
Gregory A. Margulis
Keyword(s):  
Ergodic Theorem ◽  
Curved Spaces ◽  
Nonpositively Curved ◽  
Multiplicative Ergodic Theorem

ON THE ABSOLUTE REGULARITY OF LINEAR RANDOM DYNAMICAL SYSTEMS

2003 ◽  
Vol 03 (04) ◽  
pp. 453-461 ◽  
Author(s):  
LUU HOANG DUC
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theorem ◽  
Random Dynamical Systems ◽  
Absolute Regularity ◽  
Integrability Conditions ◽  
Multiplicative Ergodic Theorem ◽  
Lyapunov Regularity ◽  
The Absolute

We introduce a concept of absolute regularity of linear random dynamical systems (RDS) that is stronger than Lyapunov regularity. We prove that a linear RDS that satisfies the integrability conditions of the multiplicative ergodic theorem of Oseledets is not merely Lyapunov regular but absolutely regular.

scholarly journals Notes on the multiplicative ergodic theorem

2017 ◽  
Vol 39 (5) ◽  
pp. 1153-1189 ◽  
Author(s):  
SIMION FILIP
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theorem ◽  
Basic Result ◽  
Multiplicative Ergodic Theorem ◽  
Summer Schools

The Oseledets multiplicative ergodic theorem is a basic result with numerous applications throughout dynamical systems. These notes provide an introduction to this theorem, as well as subsequent generalizations. They are based on lectures at summer schools in Brazil, France, and Russia.

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