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Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents
Multifractal analysis of some multiple ergodic averages non-constant Lyapunov exponents Dynamical Systems
2012/6/27
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...
Random Sequences and Pointwise Convergence of Multiple Ergodic Averages
Ergodic averages mean convergence pointwise convergence multiple recurrence
2011/1/18
We prove pointwise convergence, as N ! 1, for the multiple ergodic averages 1 N PN n=1 f(T nx) ·g(Sanx), where T and S are commuting measure preserving transformations,and an is a random version of th...
Let (X, {\cal F}, l) be the unit circle \Bbb S1 = \{z \in \Bbb C : |z| = 1\} with the usual s-algebra {\cal F} of Lebesgue measurable subsets and the normalized Lebesgue measure l. Consider a sequence...