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This paper proposes a deterministic model for the spread of an epidemic. We extend the classical Kermack–McKendrick model, so that a more general contact rate is chosen and a vaccination added. The model is governed by a differential equation (DE) for the time dynamics of the susceptibles, infectives and removals subpopulation. We present some conditions on the existence and uniqueness of a solution to the nonlinear DE. The existence of limits and uniqueness of maximum of infected individuals are...
We study a diophantine property for translation surfaces, defined in terms of saddle connections and inspired by classical Khinchin condition. We prove that the same dichotomy holds as in Khinchin theorem, then we deduce a sharp estimate on how fast the typical Teichmüller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.
I shall present some recent work in collaboration with S. Gutierrez on the characterization of all selfsimilar solutions of the binormal flow : which preserve the length parametrization. Above is a curve in , the arclength parameter, and denote the temporal variable. This flow appeared for the first time in the work of Da Rios (1906) as a crude approximation to the evolution of a vortex filament under Euler equation, and it is intimately related to the focusing cubic nonlinear Schrödinger...
We investigate the symbolic dynamics for the double standard maps of the circle onto itself, given by , where b = 1 and a is a real parameter, 0 ≤ a < 1.
We establish an upper bound on the Kolmogorov’s entropy of the locally compact attractor for strongly damped wave equation posed in locally uniform spaces in subcritical case using the method of trajectories.
We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.
Soit un feuilletage singulier d’une surface compacte . Pour analyser la dynamique de , on décompose de façon canonique en sous-surfaces bordées par des courbes transverses à : les composantes de la récurrence de (ensembles quasiminimaux) sont contenues dans les “régions de récurrence” et peuvent être étudiées séparément; par contre dans les autres régions, dites “régions de passage”, la dynamique est triviale. On propose ensuite une définition des feuilletages singuliers de classe sur...
Soit un endomorphisme holomorphe de . Je présenterai une construction géométrique, due à Briend et Duval, d’une mesure de probabilité ayant les propriétés suivantes : reflète la distribution des préimages des points en dehors d’un ensemble exceptionnel algébrique, les points périodiques répulsifs de s’équidistribuent par rapport à et est l’unique mesure d’entropie maximale de .
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