Bifurcation of gradient mappings possessing the Palais-Smale condition.
Bifurcation of heteroclinic orbits for diffeomorphisms
The paper deals with the bifurcation phenomena of heteroclinic orbits for diffeomorphisms. The existence of a Melnikov-like function for the two-dimensional case is shown. Simple possibilities of the set of heteroclinic points are described for higherdimensional cases.
Bifurcation of multi-bump homoclinics in systems with normal and slow variables.
Bifurcation of periodic and chaotic solutions in discontinuous systems
Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given...
Bifurcation of periodic orbits of time dependent Hamiltonian systems on symplectic manifolds.
Bifurcation of solutions of separable parameterized equations into lines.
Bifurcation results for a class of perturbed Fredholm maps.
Bifurcation routes to chaos in an extended Van der Pol's equation applied to economic models.
Bifurcation sequences in the dissipative systems with saddle equilibria
Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system.
In this paper we consider a class of perturbation of a Hamiltonian cubic system with 9 finite critical points. Using detection functions, we present explicit formulas for the global and local bifurcations of the flow. We exhibit various patterns of compound eyes of limit cycles. These results are concerned with the weakened Hilbert's 16th problem posed by V. I. Arnold in 1977.
Bifurcation Theory for Symmetric Potential Operators and the Equvariant Cup-length.
Bifurcations and Attractors in Bogdanov Map
Bifurcations and global stability of families of gradients
Bifurcations and Hamilton's Principle.
Bifurcations and stability of families of diffeomorphisms
Bifurcations de points fixes elliptiques
Bifurcations de points fixes elliptiques - I. Courbes invariantes
Bifurcations de points fixes elliptiques. II. Orbites périodiques et ensembles de Cantor invariants.
Bifurcations de points fixes elliptiques - III. Orbites périodiques de «petites» périodes et élimination résonnante des couples de courbes invariantes
Bifurcations de polycycles infinis pour les champs de vecteurs polynomiaux du plan