A method of reduction for invariant curves of quasiperiodically forced maps

TL;DR

This paper proves the existence of invariant and translated curves in quasiperiodically forced maps with mild regularity assumptions, characterizing their stability and bifurcations through a scalar bifurcation equation.

Contribution

It introduces a new method to establish invariant curves for quasiperiodically forced maps with rotation numbers of constant type, linking their existence to a scalar bifurcation framework.

Findings

Existence of translated and invariant curves under mild regularity conditions.

Characterization of invariant curves via a scalar bifurcation equation.

Description of stability and bifurcation behavior of these curves.

Abstract

The existence of translated curves for quasiperiodically forced maps is established, under very mild regularity hypotheses, for rotation numbers of constant type. Among the translated curves, the invariant curves are characterized as the solutions of a scalar bifurcation equation, from which their existence, stability as well as bifurcation can be easily described.