Multidimensional Rovella-like attractors

TL;DR

This paper constructs a multidimensional flow with a Rovella-like attractor exhibiting complex dynamics, non-uniform expansion, and physical measures, extending known 3D phenomena to higher dimensions with non-robust properties.

Contribution

It introduces a new class of multidimensional dynamics with Rovella-like attractors, demonstrating their existence, properties, and persistence along submanifolds, using advanced hyperbolic and Benedicks-Carleson techniques.

Findings

Existence of multidimensional Rovella-like attractors with physical measures

Construction of partially hyperbolic multidimensional dynamics

Application of Benedicks-Carleson arguments to prove non-uniform expansion

Abstract

We present a multidimensional flow exhibiting a Rovella-like attractor: a transitive invariant set with a non-Lorenz-like singularity accumulated by regular orbits and a multidimensional non-uniformly expanding invariant direction. Moreover, this attractor has a physical measure with full support but persists along certain0909.1033 submanifolds of the space of vector fields. As in the 3-dimensional Rovella-like attractor, this example is not robust. The construction introduces a class of multidimensional dynamics, whose suspension provides the Rovella-like attractor, which are partially hyperbolic, and whose quotient over stable leaves is a multidimensional endomorphism to which Benedicks-Carleson type arguments are applied to prove non-uniform expansion.