The second-order quadratic family.
The Semiclassical Electron in a Magnetic Field and Lattice. Some Problems of Low Dimensional "Periodic" Topology.
The shadowing chain lemma for singular Hamiltonian systems involving strong forces
We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.
The size of the chain recurrent set for generic maps on an n-dimensional locally (n-1)-connected compact space
For n ≥ 1, given an n-dimensional locally (n-1)-connected compact space X and a finite Borel measure μ without atoms at isolated points, we prove that for a generic (in the uniform metric) continuous map f:X → X, the set of points which are chain recurrent under f has μ-measure zero. The same is true for n = 0 (skipping the local connectedness assumption).
The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent
The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of...
The ?-Stability Theorem for Flows.
The statistical equilibrium of an isotropic stochastic flow with negative Lyapounov exponents is trivial
The structure of iteration groups of continuous functions.
The structure of Lorenz attractors
The structure of -limit sets for continuous maps of the interval
We prove that every infinite nowhere dense compact subset of the interval is an -limit set of homoclinic type for a continuous function from to .
The tiered Aubry set for autonomous Lagrangian functions
Let be a Tonelli Lagrangian function (with compact and connected and ). The tiered Aubry set (resp. Mañé set) (resp. ) is the union of the Aubry sets (resp. Mañé sets) (resp. ) for closed 1-form. Then1.the set is closed, connected and if , its intersection with any energy level is connected and chain transitive;2.for generic in the Mañé sense, the sets and have no interior;3.if the interior of is non empty, it contains a dense subset of periodic points.We then give an example...
The topology of holomorphic flows with singularity
The topology of integrable differential forms near a singularity
The zeta functions of Ruelle and Selberg. I
Time Dependent Stable Diffeomorphisms.
Topological and measurable dynamics of Lorenz maps [Book]
Topological Classification and Bifurcations of Holomorphic Flows with Resonances in ...2.
Topological Classification of Linear Endomorphisms.
Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere
This article presents a theorem about the topological conjugacy of a gradient dynamical system with a constant time step and the cascade generated by its Euler method. It is shown that on the two-dimensional sphere S² the gradient dynamical flow is, under some natural assumptions, correctly reproduced by the Euler method for a sufficiently small time step. This means that the time-map of the induced dynamical system is globally topologically conjugate to the discrete dynamical system obtained via...
Topological pressure for geodesic flows