A continuation principle for a class of periodically perturbed autonomous systems

TL;DR

This paper investigates the topological index of periodic solutions in autonomous systems with periodic perturbations, extending bifurcation analysis without requiring the perturbation to be differentiable.

Contribution

It introduces a continuation principle for a class of periodically perturbed autonomous systems, broadening bifurcation theory by removing the differentiability assumption on perturbations.

Findings

Topological index of periodic solutions evaluated

Extension of bifurcation results without differentiability assumption

Provides a new continuation principle for perturbed systems

Abstract

In this paper we evaluate the topological index of periodic solutions otained via the Malkin-Loud bifurcation result. Incidentally, we do not assume that the perturbation is differentiale.