Homoclinic orbit solutions of a one dimensional Wilson-Cowan type model.
Homoclinic tangencies and hyperbolicity for surface diffeomorphisms.
Homoclinics : Poincaré-Melnikov type results via a variational approach
Homogeneous polynomial vector fields of degree 2 on the 2-dimensional sphere.
Let X be a homogeneous polynomial vector field of degree 2 on S2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S2, and at most there are two invariant circles. We characterize the global phase portrait of these vector fields. Moreover, we show that if X has at least an invariant circle then it does not have limit cycles.
Homotopical dynamics II : Hopf invariants, smoothings and the Morse complex
Hyperbolic sets with the strong limit shadowing property.
Hyperbolicity, stability, and the criterion of homoclinic points.
Identification of quasiperiodic processes in the vicinity of the resonance
In nonlinear dynamical systems, strong quasiperiodic beating effects appear due to combination of self-excited and forced vibration. The presence of symmetric or asymmetric beatings indicates an exchange of energy between individual degrees of freedom of the model or by multiple close dominant frequencies. This effect is illustrated by the case of the van der Pol equation in the vicinity of resonance. The approximate analysis of these nonlinear effects uses the harmonic balance method and the multiple...
Index filtrations and Morse decompositions for discrete dynamical systems
On a Morse decomposition of an isolated invariant set of a homeomorphism (discrete dynamical system) there are partial orderings defined by the homeomorphism. These are called admissible orderings of the Morse decomposition. We prove the existence of index filtrations for admissible total orderings of a Morse decomposition and introduce the connection matrix in this case.
Induced expansion for quadratic polynomials
Inégalités a priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques
Infinitely many coexisting strange attractors
Infinitely many homoclinic orbits for Hamiltonian systems with group symmetries.
Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field
Integrable hierarchy of higher nonlinear Schrödinger type equations.
Integral equations and exponential trichotomy of skew-product flows.
Integrals for holomorphic foliations with singularities having all leaves compact
We show that for a holomorphic foliation with singularities in a projective variety such that every leaf is quasiprojective, the set of rational functions that are constant on the leaves form a field whose transcendence degree equals the codimension of the foliation.
Interactions entre bifurcation par brisure partielle de symétrie sphérique
Intertwined mappings
Invariance of Poincaré-Lyapunov polynomials under the group of rotations.