scholarly journals A remark on the Birkhoff ergodic theorem

1971 ◽  
Vol 15 (1) ◽  
pp. 77-79 ◽  
Author(s):  
Donald Ornstein
Keyword(s):  
Ergodic Theorem ◽  
Birkhoff Ergodic Theorem

scholarly journals A Note on the Birkhoff Ergodic Theorem

2017 ◽  
Vol 72 (1-2) ◽  
pp. 715-730
Author(s):  
Nikola Sandrić
Keyword(s):  
Ergodic Theorem ◽  
Birkhoff Ergodic Theorem

scholarly journals Ergodic theory of one dimensional Map

2012 ◽  
Vol 47 (3) ◽  
pp. 321-326
Author(s):  
HR Biswas ◽  
MS Islam
Keyword(s):  
Ergodic Theorem ◽  
Ergodic Theory ◽  
Dynamical Behavior ◽  
Ergodic Measure ◽  
One Dimensional ◽  
Birkhoff’S Ergodic Theorem ◽  
Linear Maps ◽  
Non Linear ◽  
Birkhoff Ergodic Theorem

In this paper we study one dimensional linear and non-linear maps and its dynamical behavior. We study measure theoretical dynamical behavior of the maps. We study ergodic measure and Birkhoff ergodic theorem. Also, we study some problems using Birkhoff's ergodic theorem. DOI: http://dx.doi.org/10.3329/bjsir.v47i3.13067 Bangladesh J. Sci. Ind. Res. 47(3), 321-326 2012

Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem

2019 ◽  
Vol 106 (1-2) ◽  
pp. 52-62
Author(s):  
A. G. Kachurovskii ◽  
I. V. Podvigin
Keyword(s):  
Rate Of Convergence ◽  
Ergodic Theorem ◽  
Birkhoff Ergodic Theorem

scholarly journals Weighted Birkhoff ergodic theorem with oscillating weights

2017 ◽  
Vol 39 (5) ◽  
pp. 1275-1289 ◽  
Author(s):  
AI-HUA FAN
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theorem ◽  
Almost Everywhere ◽  
Birkhoff Ergodic Theorem ◽  
Good Sequences

We consider sequences of Davenport type or Gelfond type and prove that sequences of Davenport exponent larger than$\frac{1}{2}$are good sequences of weights for the ergodic theorem, and that the ergodic sums weighted by a sequence of strong Gelfond property are well controlled almost everywhere. We prove that for any$q$-multiplicative sequence, the Gelfond property implies the strong Gelfond property and that sequences realized by dynamical systems can be fully oscillating and have the Gelfond property.

scholarly journals Strong Birkhoff ergodic theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kai Tao
Keyword(s):  
Lyapunov Exponent ◽  
Ergodic Theorem ◽  
Hölder Condition ◽  
Hölder Continuous ◽  
Subharmonic Functions ◽  
Birkhoff Ergodic Theorem ◽  
Special Case ◽  
Coupling Number

<p style='text-indent:20px;'>In this paper, we first prove the strong Birkhoff Ergodic Theorem for subharmonic functions with the irrational shift on the Torus. Then, we apply it to the analytic quasi-periodic Jacobi cocycles and show that for suitable frequency and coupling number, if the Lyapunov exponent of these cocycles is positive at one point, then it is positive on an interval centered at this point and Hölder continuous in <inline-formula><tex-math id="M1">\begin{document}$ E $\end{document}</tex-math></inline-formula> on this interval. What's more, if the coupling number of the potential is large, then the Lyapunov exponent is always positive for all irrational frequencies and Hölder continuous in <inline-formula><tex-math id="M2">\begin{document}$ E $\end{document}</tex-math></inline-formula> for all finite Liouville frequencies. For the Schrödinger cocycles, a special case of the Jacobi ones, its Lyapunov exponent is also Hölder continuous in the frequency and the lengths of the intervals where the Hölder condition of the Lyapunov exponent holds only depend on the coupling number.</p>

Sign in / Sign up

Export Citation Format

Share Document