Localized induction equation for stretched vortex filament.
Locally conformal cosymplectic manifolds and time-dependent Hamiltonian systems
We show that locally conformal cosymplectic manifolds may be seen as generalized phase spaces of time-dependent Hamiltonian systems. Thus we extend the results of I. Vaisman for the time-dependent case.
Locally connected exceptional minimal sets of surface homeomorphisms
We deal with locally connected exceptional minimal sets of surface homeomorphisms. If the surface is different from the torus, such a minimal set is either finite or a finite disjoint union of simple closed curves. On the torus, such a set can admit also a structure similar to that of the Sierpiński curve.
Locally equicontinuous dynamical systems
A new class of dynamical systems is defined, the class of “locally equicontinuous systems” (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems....
Logarithmic convexity of push-forward measures.
Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
This paper is devoted to the study of a coupled system which consists of a wave equation and a heat equation coupled through a transmission condition along a steady interface. This system is a linearized model for fluid-structure interaction introduced by Rauch, Zhang and Zuazua for a simple transmission condition and by Zhang and Zuazua for a natural transmission condition. Using an abstract theorem of Burq and a new Carleman estimate proved near the interface, we complete the results obtained...
Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
This paper is devoted to the study of a coupled system which consists of a wave equation and a heat equation coupled through a transmission condition along a steady interface. This system is a linearized model for fluid-structure interaction introduced by Rauch, Zhang and Zuazua for a simple transmission condition and by Zhang and Zuazua for a natural transmission condition. Using an abstract theorem of Burq and a new Carleman estimate proved near the interface, we complete the results obtained...
Logarithmic frequency in morphic sequences
We study the logarithmic frequency of letters and words in morphic sequences and show that this frequency must always exist, answering a question of Allouche and Shallit.
Logarithmic measures, subdimension and Lyapunov exponents of Cantori
Logistic population change and the Mankiw-Romer-Weil model.
Long time asymptotics of the Camassa–Holm equation on the half-line
We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation on the half-line . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane , having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data...
Long time behaviour and stationary regime of memory gradient diffusions
In this paper, we are interested in a diffusion process based on a gradient descent. The process is non Markov and has a memory term which is built as a weighted average of the drift term all along the past of the trajectory. For this type of diffusion, we study the long time behaviour of the process in terms of the memory. We exhibit some conditions for the long-time stability of the dynamical system and then provide, when stable, some convergence properties of the occupation measures and of the...
Long time dynamics for the one dimensional non linear Schrödinger equation
In this article, we first present the construction of Gibbs measures associated to nonlinear Schrödinger equations with harmonic potential. Then we show that the corresponding Cauchy problem is globally well-posed for rough initial conditions in a statistical set (the support of the measures). Finally, we prove that the Gibbs measures are indeed invariant by the flow of the equation. As a byproduct of our analysis, we give a global well-posedness and scattering result for the critical and super-critical...
Looking for the Bernoulli shift
Loop groups and equations of KdV type
Lorenz attractor through saddle-node bifurcations
Lower and upper bounds for the splitting of separatrices of a pendulum under a fast quasiperiodic forcing.
Lyapunov center theorem for some nonlinear PDE's : a simple proof
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
Lyapunov exponents for higher dimensional random maps.