Towards a renormalization theory for quasi-periodically forced one dimensional maps III. Numerical Support

TL;DR

This paper provides numerical evidence supporting conjectures in a renormalization theory for quasi-periodically forced one-dimensional maps, enhancing understanding of self-similarity and universality in these systems.

Contribution

It offers numerical validation for previously unproven conjectures in the renormalization framework for quasi-periodic maps, extending the theory's credibility.

Findings

Numerical support for four key conjectures in the theory.

Enhanced understanding of self-similarity in Forced Logistic Maps.

Discussion on the applicability of the theory to specific systems.

Abstract

In a previous work by the authors the one dimensional (doubling) renormalization operator was extended to the case of quasi-periodically forced one dimensional maps. The theory was used to explain different self-similarity and universality observed numerically in the parameter space of the Forced Logistic Maps. The extension proposed was not complete in the sense that we assumed a total of four conjectures to be true. In this paper we present numerical support for these conjectures. We also discuss the applicability of this theory to the Forced Logistic Map.