About some theorems by L. P. Šil'nikov
Absolute Stability and Bifurcation Theory.
Action-angle coordinates at singularities for analytic integrable systems.
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings. (Summary).
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings.
An approach to robust control of the Hopf bifurcation.
An attraction result and an index theorem for continuous flows on
We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on for which is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in EE such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on .
An extension of the Artin-Mazur theorem.
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
Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry
Here we present basic ideas and algorithms of Power Geometry and give a survey of some of its applications. In Section 2, we consider one generic ordinary differential equation and demonstrate how to find asymptotic forms and asymptotic expansions of its solutions. In Section 3, we demonstrate how to find expansions of solutions to Painlevé equations by this method, and we analyze singularities of plane oscillations of a satellite on an elliptic orbit. In Section 4, we consider the problem of local...
Application of the Lyapunov-Schmidt method to the problem of the branching of a cycle from a family of equilibria in a system with multicosymmetry.
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
Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schrödinger equation.
Bifurcation analysis of a van der Pol-Duffing circuit with parallel resistor.
Bifurcation analysis of the Hénon map.