Mean Li-Yorke chaos along polynomials of several variables and prime numbers

TL;DR

This paper demonstrates that in topological dynamical systems with positive entropy, mean Li-Yorke chaos occurs along non-constant polynomials of multiple variables and prime numbers, based on the analysis of ergodic averages.

Contribution

It establishes a link between positive entropy and mean Li-Yorke chaos along complex polynomial sequences in multiple variables and primes, extending previous results.

Findings

Positive entropy implies mean Li-Yorke chaos along polynomial sequences.

Chaos occurs along non-constant polynomials of several variables and prime numbers.

The proof involves analyzing the limiting behavior of ergodic averages.

Abstract

In this paper, for any given polynomial, by analyzing the limiting behavior of ergodic averages along polynomials of several variables and prime numbers, we prove that for a topology dynamical system, positive entropy implies mean Li-Yoke chaos along non-constant polynomials of several variables and prime numbers.