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4 - Probability (Finite) Invariant Measures: Finer Properties

from Part I - Ergodic Theory and Geometric Measures

Published online by Cambridge University Press:  20 April 2023

Janina Kotus  and
Mariusz Urbański
Janina Kotus
Affiliation:
Warsaw University of Technology
Mariusz Urbański
Affiliation:
University of North Texas
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Summary

We deal, in this chapter, with refined stochastic laws for dynamical systems preserving an infinite measure. This is primarily the Darling–Kac Theorem. We make use of some recent progress on this theorem and related issues, mainly due to Zweimüller, Thaler, Theresiu, Melbourne, Gouëzel, Bruin, Aaronson, and others, but we do not go into the most recent subtleties and developments of this branch of infinite ergodic theory. We do not need them for our applications to elliptic functions.

Keywords

Infinite invariant measuresDarling–Kac Theorempoints of infinite condensation
Type
Chapter
Information
Meromorphic Dynamics
Abstract Ergodic Theory, Geometry, Graph Directed Markov Systems, and Conformal Measures
 , pp. 122 - 133
Publisher: Cambridge University Press
Print publication year: 2023

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