Ergodic Theory and Connections with Analysisand
نویسنده
چکیده
In this paper we establish a variety or results in ergodic theory by using techniques from probability and analysis. We discuss divergence of operators, including strong sweeping out and Bourgain's entropy method. We consider square functions, oscillation operators, and variational operators for ergodic averages. We also consider almost everywhere convergence of convo-lution powers.
منابع مشابه
Poisson suspensions and infinite ergodic theory
We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaus...
متن کامل2 6 Fe b 20 08 POISSON SUSPENSIONS AND INFINITE ERGODIC THEORY
We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaus...
متن کاملJa n 20 08 POISSON SUSPENSIONS AND INFINITE ERGODIC THEORY
We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure preserving ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar l...
متن کاملErgodic Theory and Connections with Analysis and Probability
In this paper we establish a variety or results in ergodic theory by using techniques from probability and analysis. We discuss divergence of operators, including strong sweeping out and Bourgain’s entropy method. We consider square functions, oscillation operators, and variational operators for ergodic averages. We also consider almost everywhere convergence of convolution powers.
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This paper reviews connections of the 3x + 1 mapping and its generalizations with ergodic theory and Markov chains. The work arose out of efforts to describe the observed limiting frequencies of divergent trajectories in the congruence classes (mod m).
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