Difféomorphismes pseudo-Anosov et automorphismes symplectiques de l'homologie
Diffeomorphisms with Invariant Line Bundles.
Diffeomorphisms with weak shadowing
The weak shadowing property is really weaker than the shadowing property. It is proved that every element of the C¹ interior of the set of all diffeomorphisms on a closed surface having the weak shadowing property satisfies Axiom A and the no-cycle condition (this result does not generalize to higher dimensions), and that the non-wandering set of a diffeomorphism f belonging to the C¹ interior is finite if and only if f is Morse-Smale.
Different types of scaling in the dynamics of period-doubling maps under external periodic driving.
Différentiabilité des conjugaisons entre systèmes dynamiques de dimension 1
Si deux systèmes dynamiques de dimension 1 et de classe sont -conjugués, dans quelles conditions sont-ils -conjugués ? Par “système dynamique de dimension 1”, nous entendons ici un feuilletage de codimension 1 ou une application du cercle dans lui-même. Nous donnons des conditions très faibles pour que la réponse à la question précédente soit positive.
Differentiability and analycity of topological entropy for Anosov and geodesic flows.
Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation
We consider a stochastic Burgers equation. We show that the gradient of the corresponding transition semigroup does exist for any bounded ; and can be estimated by a suitable exponential weight. An application to some Hamilton-Jacobi equation arising in Stochastic Control is given.
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows
Differentiable rigidity and smooth conjugacy.
Differentiable semiflows for differential equations with state-dependent delays.
Differential and integral calculus for a Schauder basis on a fractal set (I) (Schauder basis 80 years after)
In this paper we introduce a concept of Schauder basis on a self-similar fractal set and develop differential and integral calculus for them. We give the following results: (1) We introduce a Schauder/Haar basis on a self-similar fractal set (Theorems I and I'). (2) We obtain a wavelet expansion for the L²-space with respect to the Hausdorff measure on a self-similar fractal set (Theorems II and II'). (3) We introduce a product structure and derivation on a self-similar fractal set (Theorem III)....
Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems
We consider the problem of Arnold’s diffusion for nearly integrable isochronous Hamiltonian systems. We prove a shadowing theorem which improves the known estimates for the diffusion time. We also justify for three time scales systems that the splitting of the separatrices is correctly predicted by the Poincaré-Melnikov function.
Diffusion times and stability exponents for nearly integrable analytic systems
For a positive integer n and R>0, we set . Given R>1 and n≥4 we construct a sequence of analytic perturbations (H j) of the completely integrable Hamiltonian on , with unstable orbits for which we can estimate the time of drift in the action space. These functions H j are analytic on a fixed complex neighborhood V of , and setting the time of drift of these orbits is smaller than (C(1/ɛ j)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly resonant surface,...
Diffusion to infinity for periodic orbits in meromorphic dynamics
A small perturbation of a rational function causes only a small perturbation of its periodic orbits. We show that the situation is different for transcendental maps. Namely, orbits may escape to infinity under small perturbations of parameters. We show examples where this "diffusion to infinity" occurs and prove certain conditions under which it does not.
Diffusive instability in a prey-predator system with time-dependent diffusivity.
Diffusive synchronization of hyperchaotic Lorenz systems.
Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems
We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory and provide...
Dilation of a class of quantum dynamical semigroups with unbounded generators on UHF algebras
Dimension and product structure of hyperbolic measures.
Dimension groups for interval maps.