An approach to robust control of the Hopf bifurcation.
An index for global Hopf bifurcation in parabolic systems.
An Index Theory and Existence of Multiple Brake Orbits for Star-Shaped Hamiltonian Systems
An -equivariant degree and the Fuller index
Applications numériques de la dualité en mécanique hamiltonienne
Applications of symplectic homology II: Stability of the action spectrum.
Applications of the Euler characteristic in bifurcation theory.
Let f: Rn x Rn → Rn be a continuous map such that f(0,λ) = 0 for all λ ∈ Rk. In this article we formulate, in terms of the Euler characteristic of algebraic sets, sufficient conditions for the existence of bifurcation points of the equation f(x,λ) = 0. Moreover we apply these results in bifurcation theory to ordinary differential equations. It is worth to point out that in the last paragraph we show how to verify, by computer, the assumptions of the theorems of this paper.
Asymmetric bound states of differential equations in nonlinear optics
Bifurcation analysis of a van der Pol-Duffing circuit with parallel resistor.
Bifurcation and stability of families of hyperbolic vector fields in dimension three
Bifurcation de cycles limites au voisinage de polycycles hyperboliques et génériques à trois sommets
Bifurcation d'orbites homoclines pour les systèmes hamiltoniens
Bifurcation d'orbites périodiques d'un système hamiltonien au voisinage d'une position d'équilibre
Bifurcation of contracting singular cycles
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 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 global stability of families of gradients