# Robust degenerate unfoldings of cycles and tangencies

## TL;DR

This paper constructs open sets of degenerate unfoldings of heterodimensional cycles and homoclinic tangencies of arbitrary codimension, revealing complex phenomena like coexistence of infinitely many attractors in dynamical systems.

## Contribution

It introduces new methods to create robust degeneracies in dynamical systems, including tangencies of large codimension outside strong hyperbolic sets.

## Key findings

- Support for coexistence of infinitely many attractors
- Construction of robust homoclinic tangencies of large codimension
- Identification of phenomena outside strong hyperbolic sets

## Abstract

We construct open sets of degenerate unfoldings of heterodimensional cycles of any co-index $c>0$ and homoclinic tangencies of arbitrary codimension $c>0$. These sets are known to be the support of unexpected phenomena in families of diffeomorphisms, such as the Kolmogorov typical co-existence of infinitely many attractors. As a prerequisite we also construct robust homoclinic tangencies of large codimension which cannot be inside a strong partially hyperbolic set.