Perturbations of quadratic Hamiltonian two-saddle cycles

TL;DR

This paper establishes an upper bound of three on the number of limit cycles that can bifurcate from a two-saddle loop in a quadratic Hamiltonian system under quadratic perturbations.

Contribution

It provides a new upper bound for bifurcating limit cycles in quadratic Hamiltonian systems with two-saddle loops under quadratic deformations.

Findings

Maximum of three bifurcating limit cycles from a two-saddle loop.

Bound holds for arbitrary quadratic perturbations.

Advances understanding of bifurcation behavior in quadratic Hamiltonian systems.

Abstract

We prove that the number of limit cycles, which bifurcate from a two-saddle loop of a planar quadratic Hamiltonian system, under an arbitrary quadratic deformation, is less than or equal to three.