$C^2$-robust heterodimensional tangencies

TL;DR

This paper establishes conditions for the existence of $C^{2}$ robust heterodimensional tangencies and constructs an open set of diffeomorphisms with such tangencies forming part of a robust cycle.

Contribution

It provides the first sufficient conditions for $C^{2}$ robust heterodimensional tangencies and constructs an open set of diffeomorphisms exhibiting these tangencies.

Findings

Existence of $C^{2}$ robust heterodimensional tangencies under certain conditions

Construction of an open set in $ ext{Diff}^2(M)$ with robust heterodimensional cycles

Demonstration of non-degenerate heterodimensional tangencies in the constructed set

Abstract

In this paper, we give sufficient conditions for the existence of $C^{2}$ robust heterodimensional tangency, and present a nonempty open set in $\Diff^2(M)$ with $\dim(M)\geq 3$ each element of which has a non-degenerate heterodimensional tangency on a $C^2$ robust heterodimensional cycle.