Exponential of a hamiltonian in large subsets of a lattice and applications
Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov’s second method
In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering processes...
Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method
In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov's second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering processes...
Exponentially long time stability for non-linearizable analytic germs of .
We study the Siegel-Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey-, category. We introduce a new arithmetical condition of Bruno type on the linear part of the given germ, which ensures the existence of a Gevrey- formal linearization. We use this fact to prove the effective stability, i.e. stability for finite but long time, of neighborhoods of the origin, for the analytic germ.
Exposants caractéristiques de l'algorithme de Jacobi-Perron et de la transformation associée
On montre que les exposants de Lyapunov de l’algorithme de Jacobi-Perron, en dimension quelconque, sont tous différents et que la somme des exposants extrêmes est strictement positive. En particulier, si , le deuxième exposant est strictement négatif.
Extended dynamical systems.
Extensions of probability-preserving systems by measurably-varying homogeneous spaces and applications
We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such extensions rests on a simple notion of 'direct integral' for a 'measurable family' of homogeneous spaces, which has a number of precedents in older literature. The main contribution of the present paper is the systematic development of a formalism for handling such extensions,...
Extensions of symplectic groupoids and quantization.
Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances
A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]....
Extreme Relations for Topological Flows
We introduce the concept of an extreme relation for a topological flow as an analogue of the extreme measurable partition for a measure-preserving transformation considered by Rokhlin and Sinai, and we show that every topological flow has such a relation for any invariant measure. From this result, it follows, among other things, that any deterministic flow has zero topological entropy and any flow which is a K-system with respect to an invariant measure with full support is a topological K-flow....
-manifolds and integrable systems of hydrodynamic type
We investigate the role of Hertling-Manin condition on the structure constants of an associative commutative algebra in the theory of integrable systems of hydrodynamic type. In such a framework we introduce the notion of -manifold with compatible connection generalizing a structure introduced by Manin.
Faà di Bruno's formula and nonhyperbolic fixed points of one-dimensional maps.
Factorisation of Lefschetz zeta functions and twisted periodic orbits.
Factors and Extensions of Full Shifts.
Failure of convergence of the Lax-Oleinik semi-group in the time periodic case
Faithful zero-dimensional principal extensions
We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν | X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the authors' result in Acta Appl. Math. [to appear] (where the extension was principal, but not necessarily faithful).
Families of whiskered tori for a-priori stable/unstable Hamiltonian systems and construction of unstable orbits.
Fano manifolds of degree ten and EPW sextics
O’Grady showed that certain special sextics in called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.
Far from equilibrium computation and particle swarm optimization.
Farey curves.