showing 2 related works from this author
Alien limit cycles near a Hamiltonian 2-saddle cycle
2005
Abstract It is known that perturbations from a Hamiltonian 2-saddle cycle Γ can produce limit cycles that are not covered by the Abelian integral, even when it is generic. These limit cycles are called alien limit cycles. This phenomenon cannot appear in the case that Γ is a periodic orbit, a non-degenerate singularity, or a saddle loop. In this Note, we present a way to study this phenomenon in a particular unfolding of a Hamiltonian 2-saddle cycle, keeping one connection unbroken at the bifurcation. To cite this article: M. Caubergh et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).
Canard Cycles with Three Breaking Mechanisms
2016
This article deals with relaxation oscillations from a generic balanced canard cycle \(\Gamma\) subject to three breaking parameters of Hopf or jump type. We prove that in a rescaled layer of \(\Gamma\) there bifurcate at most five relaxation oscillations.