Exact Statistics of Chaotic Dynamical Systems

TL;DR

This paper introduces an inverse method for constructing chaotic invariant sets with exact statistical properties, potentially applicable to classical and quantum systems.

Contribution

It presents a novel inverse approach to determine chaotic invariant sets and their exact statistics, extending classical methods and suggesting applications in quantum field theory.

Findings

Constructed large classes of chaotic invariant sets with exact statistics

Developed an inverse method characterized by a probability distribution and a two-form

Suggested potential applications to quantum field theory and stochastic quantization

Abstract

We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is on classical systems, we briefly speculate about possible applications to quantum field theory, in the context of generalizations of stochastic quantization.