On the number of limit cycles which appear by perturbation of Hamiltonian two-saddle cycles of planar vector fields

TL;DR

This paper establishes an upper limit on the number of limit cycles that can emerge from a Hamiltonian two-saddle loop in planar vector fields when subjected to analytic perturbations.

Contribution

It provides a new upper bound for limit cycles bifurcating from Hamiltonian two-saddle loops under analytic deformation, advancing understanding of bifurcation phenomena.

Findings

Derived an explicit upper bound for bifurcating limit cycles.

Applied the bound to specific classes of planar vector fields.

Enhanced the theoretical framework for analyzing Hamiltonian bifurcations.

Abstract

We find an upper bound to the maximal number of limit cycles, which bifurcate from a hamiltonian two-saddle loop of an analytic vector field, under an analytic deformation.