Critical attractors and q-statistics

TL;DR

This paper explores the properties of one-dimensional critical attractors related to the three main routes to chaos, linking them to systems with many degrees of freedom at transitional states, within the framework of q-statistics.

Contribution

It provides an analysis of critical attractors across different routes to chaos and connects their features to complex systems at extremal or transitional conditions, using q-statistics.

Findings

Features of critical attractors are characterized within q-statistics.

Connections between low-dimensional attractors and high-dimensional systems are discussed.

Insights into the dynamics at extremal or transitional states are provided.

Abstract

An account is given of the features, of the kind pertaining to q-statistics, of the dynamics at the one-dimensional critical attractors associated to the three familiar routes to chaos, intermittency, period doubling and quasiperiodicity. Connections between the properties of these attractors and those of systems with many degrees of freedom at extremal or transitional states are briefly described.