Spectral mapping theorems and stability theory in linear dynamical systems.
Spectral properties of ergodic dynamical systems conjugate to their composition squares
Let S and T be automorphisms of a standard Borel probability space. Some ergodic and spectral consequences of the equation ST = T²S are given for T ergodic and also when Tⁿ = I for some n>2. These ideas are used to construct examples of ergodic automorphisms S with oscillating maximal spectral multiplicity function. Other examples illustrating the theory are given, including Gaussian automorphisms having simple spectra and conjugate to their squares.
Spectral properties of G-symbolic Morse shifts
Spectral properties of weakly almost periodic cosine functions
The spectral structure of the infinitesimal generator of a strongly continuous cosine function of linear bounded operators is investigated, under assumptions on the almost periodic behaviour of applications generated, in various ways, by C. Moreover, a first approach is presented to the analysis of connection between cosine functions and dynamical systems.
Spectral theta series of operators with periodic bicharacteristic flow
The theta series is a classical example of a modular form. In this article we argue that the trace , where is a self-adjoint elliptic pseudo-differential operator of order 1 with periodic bicharacteristic flow, may be viewed as a natural generalization. In particular, we establish approximate functional relations under the action of the modular group. This allows a detailed analysis of the asymptotics of near the real axis, and the proof of logarithm laws and limit theorems for its value...
Spectre des opérateurs elliptiques et flots hamiltoniens
Spectres de M-extensions aléatoires
Spectrum and generation of solutions of the Toda lattice.
Spectrum of the Poincaré Map for Periodic Reflecting Rays in Generic Domains.
Spin-stabilized spacecrafts: analytical attitude propagation using magnetic torques.
Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom.
Spreadability, Vulnerability and Protector Control
In this work, we present some concepts recently introduced in the analysis and control of distributed parameter systems: Spreadability, vulnerability and protector control. These concepts permit to describe many biogeographical phenomena, as those of pollution, desertification or epidemics, which are characterized by a spatio-temporal evolution
Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic submanifolds.
SRB measures for non-hyperbolic systems with multidimensional expansion
SRB-like Measures for C⁰ Dynamics
For any continuous map f: M → M on a compact manifold M, we define SRB-like (or observable) probabilities as a generalization of Sinai-Ruelle-Bowen (i.e. physical) measures. We prove that f always has observable measures, even if SRB measures do not exist. We prove that the definition of observability is optimal, provided that the purpose of the researcher is to describe the asymptotic statistics for Lebesgue almost all initial states. Precisely, the never empty set of all observable measures is...
Stabilité des systèmes à commutations du plan
Soient et deux champs de vecteurs lisses sur globalement asymptotiquement stables à l’origine. Nous donnons des conditions nécessaires et des conditions suffisantes sur la topologie de l’ensemble des points où et sont parallèles pour pouvoir assurer la stabilité asymptotique globale du système contrôlé non linéaire non autonomeoù le contrôle est une fonction mesurable arbitraire de dans . Les conditions données ne nécessitent aucune intégration ou construction d’une fonction de Lyapunov...
Stabilité ou instabilité des points fixes elliptiques
Stabilité structurelle
Stability and bifurcation in a simplified four-neuron bam neural network with multiple delays.
Stability and bifurcation of a class of discrete-time Cohen-Grossberg neural networks with delays.