Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points

TL;DR

This paper investigates the complex dynamics near nonhyperbolic fixed points and homoclinic tangent points, introducing new methods to analyze periodic points and shadowing phenomena in such nonhyperbolic settings.

Contribution

It presents general conditions for the existence of infinite periodic points and introduces a novel approach based on center disk dynamics.

Findings

Established conditions for infinite periodic points near nonhyperbolic points

Developed a new method using center disks for dynamical analysis

Obtained results on shadowing near nonhyperbolic fixed points

Abstract

We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of the dynamics of center disks, is introduced. Some results on shadowing near a non-hyperbolic fixed point of a homeomorphism are obtained.