Multifractal Analysis of Multiple Ergodic Averages
Ai-Hua Fan (LAMFA), Joerg Schmeling, Meng Wu (LAMFA)
TL;DR
This paper provides a comprehensive analysis of the multifractal structure of multiple ergodic averages within symbolic dynamics, focusing on functions of two variables that depend on the initial coordinate.
Contribution
It offers a complete solution to the multifractal analysis problem for a specific class of functions in symbolic dynamics, advancing understanding in ergodic theory.
Findings
Detailed multifractal spectrum characterization
Explicit formulas for Hausdorff dimensions
Extension of previous ergodic analysis results
Abstract
In this paper we present a complete solution to the problem of multifractal analysis of multiple ergodic averages in the case of symbolic dynamics for functions of two variables depending on the first coordinate.
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