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.
Magnetic flows and Gaussian thermostats on manifolds of negative curvature
We consider a class of flows which includes both magnetic flows and Gaussian thermostats of external fields. We give sufficient conditions for such flows on manifolds of negative sectional curvature to be Anosov.
Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics
I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.
Mahler measure and entropy for commuting automorphisms of compact groups.
Majorations affines du nombre de zéros d'intégrales abéliennes pour les hamiltoniens quartiques elliptiques
Maličky-Riečan's entropy as a version of operator entropy
The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.
Manin matrices, quantum elliptic commutative families and characteristic polynomial of elliptic Gaudin model.
Mapping properties of Fatou components.