Robust tangencies of large codimension

TL;DR

This paper constructs specific robust tangencies of large codimension within transitive partially hyperbolic sets, advancing the understanding of complex dynamical behaviors.

Contribution

It introduces methods to create $C^2$-robust homoclinic and heterodimensional tangencies of large codimension in partially hyperbolic systems.

Findings

Existence of $C^2$-robust tangencies of large codimension

Construction techniques within transitive partially hyperbolic sets

Enhanced understanding of complex dynamical structures

Abstract

We construct $C^2$-robust homoclinic and heterodimensional tangencies of large codimension inside transitive partially hyperbolic sets.