scholarly journals A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem

2006 ◽  
Vol 133 (1) ◽  
pp. 95-123 ◽  
Author(s):  
David Damanik ◽  
Daniel Lenz
Keyword(s):  
Uniform Convergence ◽  
Ergodic Theorem ◽  
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 Uniform Convergence of Cesaro Averages for Uniquely Ergodic C*-Dynamical Systems

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 987 ◽  
Author(s):  
Francesco Fidaleo
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Uniform Convergence ◽  
Unit Circle ◽  
Ergodic Theorem ◽  
Ergodic Theory ◽  
C Algebra ◽  
Cesaro Averages ◽  
Uniformly Convergent ◽  
Uniquely Ergodic

Consider a uniquely ergodic C * -dynamical system based on a unital *-endomorphism Φ of a C * -algebra. We prove the uniform convergence of Cesaro averages 1 n ∑ k = 0 n − 1 λ − n Φ ( a ) for all values λ in the unit circle, which are not eigenvalues corresponding to “measurable non-continuous” eigenfunctions. This result generalizes an analogous one, known in commutative ergodic theory, which turns out to be a combination of the Wiener–Wintner theorem and the uniformly convergent ergodic theorem of Krylov and Bogolioubov.

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