Giga-Periodic Orbits for Weakly Coupled Tent and Logistic Discretized Maps

TL;DR

This paper presents new models of weakly coupled logistic and tent maps that generate extremely long periodic orbits exceeding one billion in length, with analysis of their invariant measures.

Contribution

Introduction of novel weakly coupled logistic and tent map models capable of producing extremely long periodic orbits and analysis of their invariant measures.

Findings

Orbits longer than one billion periods identified

Invariant measure properties described for the models

Models demonstrate very long periodic behavior

Abstract

We introduce new models of very weakly coupled logistic and tent maps for which orbits of very long period are found. The length of these periods is far greater than one billion. The property of these models relatively to the distribution of the iterated points (invariant measure) is described.