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.
Lyapunov exponents, KS-entropy and correlation decay in skew product extensions of Bernoulli endomorphisms
Viene considerata una classe di sistemi dinamici del toro bidimensionale . Tali sistemi presentano la forma di un prodotto skew fra l'endomorfismo Bernoulli , , definito sul toro undidimensionale ed una traslazione del toro stesso. Si dimostra che gli esponenti di Liapunov e l'entropia di Kolmogorov-Sinai della misura di Haar invariante possono essere calcolati esplicitamente. Viene infine discusso il decadimento delle correlazioni per i caratteri.
Lyapunov Exponents of Rank -Variations of Hodge Structures and Modular Embeddings
If the monodromy representation of a VHS over a hyperbolic curve stabilizes a rank two subspace, there is a single non-negative Lyapunov exponent associated with it. We derive an explicit formula using only the representation in the case when the monodromy is discrete.
Lyapunov functionals construction for stochastic difference second-kind Volterra equations with continuous time.
Lyapunov Functions for Weak Solutions of Reaction-Diffusion Equations with Discontinuous Interaction Functions and its Applications
In this paper we investigate additional regularity properties for global and trajectory attractors of all globally defined weak solutions of semi-linear parabolic differential reaction-diffusion equations with discontinuous nonlinearities, when initial data uτ ∈ L2(Ω). The main contributions in this paper are: (i) sufficient conditions for the existence of a Lyapunov function for all weak solutions of autonomous differential reaction-diffusion equations with discontinuous and multivalued interaction...
Lyapunov quasi-stable trajectories
We introduce the notions of Lyapunov quasi-stability and Zhukovskiĭ quasi-stability of a trajectory in an impulsive semidynamical system defined in a metric space, which are counterparts of corresponding stabilities in the theory of dynamical systems. We initiate the study of fundamental properties of those quasi-stable trajectories, in particular, the structures of their positive limit sets. In fact, we prove that if a trajectory is asymptotically Lyapunov quasi-stable, then its limit set consists...
Lyapunov stability of closed sets in impulsive semidynamical systems.