On bifurcations of area-preserving and non-orientable maps with quadratic homoclinic tangencies

TL;DR

This paper investigates how quadratic homoclinic tangencies in non-orientable area-preserving maps lead to bifurcations and the formation of elliptic periodic orbits, expanding understanding of complex dynamics on non-orientable surfaces.

Contribution

It provides new results on bifurcations in non-orientable area-preserving maps with quadratic homoclinic tangencies, including conditions for elliptic orbit emergence.

Findings

Elliptic periodic orbits can bifurcate from quadratic homoclinic tangencies.

Results apply to one and two parameter unfoldings.

Analysis on non-orientable two-dimensional surfaces.

Abstract

We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings and establish results related to the emergence of elliptic periodic orbits.