Non-smooth saddle-node bifurcations II: dimensions of strange attractors

TL;DR

This paper investigates the geometric and topological characteristics of strange non-chaotic attractors arising from non-smooth saddle-node bifurcations in quasiperiodically forced interval maps, focusing on their dimensions and structure.

Contribution

It introduces a novel approach to analyze the dimensions and topology of strange non-chaotic attractors, revealing their Hausdorff and box-counting dimensions as distinct and describing their minimality.

Findings

Hausdorff and box-counting dimensions of attractors are distinct

The topological structure of attractors is characterized

Attractors are shown to be minimal sets

Abstract

We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of a continuous curve and controlling the geometry of the latter, we determine their Hausdorff and box-counting dimension and show that these take distinct values. Moreover, the same approach allows to describe the topological structure of the attractors and to prove their minimality.