Creation of blenders in the conservative setting

TL;DR

This paper proves that any conservative diffeomorphism with a specific hyperbolic periodic point structure can be approximated by diffeomorphisms containing blenders, advancing understanding of complex dynamical behaviors in conservative systems.

Contribution

It introduces a method to approximate conservative diffeomorphisms with blenders, expanding the toolkit for studying conservative dynamical systems.

Findings

Existence of blenders in conservative systems under certain conditions

Approximation of conservative diffeomorphisms by those with blenders

Enhancement of techniques for analyzing hyperbolic dynamics

Abstract

In this work we prove that each C^r conservative diffeomorphism with a pair of hyperbolic periodic points of co-index one can be C^1-approximated by C^r conservative diffeomorphisms having a blender.