Investigation on Bifurcation of Map Satisfying Condition of Periodic Doubling Bifurcation

TL;DR

This paper explores the conditions under which a double circle invariant appears in one-parameter discrete dynamical systems on a cylinder, focusing on bifurcation phenomena related to periodic doubling.

Contribution

It provides new sufficient conditions for the occurrence of invariant double circles in such systems, advancing understanding of bifurcation behavior.

Findings

Identifies conditions for invariant double circles

Analyzes bifurcation mechanisms in discrete systems

Contributes to bifurcation theory in dynamical systems

Abstract

In this paper, we consider sufficient conditions for an invariant double circle to occur in a one parameter discrete dynamical systems on a cylinder.