Bony attractors in higher dimension

TL;DR

This paper extends the concept of bony attractors from simple skew products to more complex diffeomorphisms on higher-dimensional tori, broadening understanding of these phenomena in dynamical systems.

Contribution

It introduces a new class of diffeomorphisms on higher-dimensional tori where bony attractors can occur, expanding the scope of previous models.

Findings

Bony attractors exist in higher-dimensional diffeomorphisms.

Extension from skew products to more general diffeomorphisms.

Demonstrates the robustness of bony attractors in complex systems.

Abstract

In this article, we extend the phenomena of a bony attractor from a rather artificial class of step skew products to the class of diffeomorphisms on the Cartesian product of the two-dimensional torus by a sphere of arbitrary dimension.