Remarks on Power Spectra of Chaotic Dynamical Systems

TL;DR

This paper introduces a new inverse method for calculating power spectra of chaotic systems using invariant distributions and two-forms, enabling efficient computation without direct simulation.

Contribution

It presents a novel inverse approach that leverages quantum field theory techniques and Monte Carlo methods to compute auto-correlation functions in chaotic systems.

Findings

Successfully applied the method to a specific example

Able to compute auto-correlation functions without direct numerical simulation

Demonstrated the use of Pade approximants for short time expansions

Abstract

We develop novel methods to compute auto-correlation functions, or power spectral densities, for chaotic dynamical systems generated by an inverse method whose starting point is an invariant distribution and a two-form. In general, the inverse method makes some aspects of chaotic dynamics calculable by methods familiar in quantum field theory. This approach has the numerical advantage of being amenable to Monte-Carlo parallel computation. We demonstrate the approach on a specific example, and show how auto-correlation functions can be computed without any direct numerical simulation, by Pade approximants of a short time expansion.