Le «closing lemma» en topologie
Le problème de la finitude du nombre de cycles limites
Le système de Hénon-Heiles
Levi-flat invariant sets of holomorphic symplectic mappings
We classify four families of Levi-flat sets which are defined by quadratic polynomials and invariant under certain linear holomorphic symplectic maps. The normalization of Levi- flat real analytic sets is studied through the technique of Segre varieties. The main purpose of this paper is to apply the Levi-flat sets to the study of convergence of Birkhoff's normalization for holomorphic symplectic maps. We also establish some relationships between Levi-flat invariant sets...
Lie-point symmetries in bifurcation problems
Limit cycles for vector fields with homogeneous components
We study planar polynomial differential equations with homogeneous components. This kind of equations present a simple and well known dynamics when the degrees (n and m) of both components coincide. Here we consider the case and we show that the dynamics is more complicated. In fact, we prove that such systems can exhibit periodic orbits only when nm is odd. Furthermore, for nm odd we give examples of such differential equations with at least (n+m)/2 limit cycles.
Limit cycles in the equation of whirling pendulum with autonomous perturbation
The two-parameter Hamiltonian system with the autonomous perturbation is considered. Via the Mel’nikov method, existence and uniqueness of a limit cycle of the system in a certain region of a two-dimensional space of parameters is proved.
Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields
We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.
Linearizability of a polynomial system
Linearization of analytic and non-analytic germs of diffeomorphisms of
Ljusternik-Schnirelman theory with local Palais-Smale condition and singular dynamical systems
Lorenz attractor through saddle-node bifurcations
Lower and upper bounds for the splitting of separatrices of a pendulum under a fast quasiperiodic forcing.
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms