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.
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,...
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]....
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....
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.
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).
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.
We show that the Fatou components of a certain transcendental entire function have a common curve in their boundaries.
Fault tolerant control for uncertain systems with time varying state-delay is studied in this paper. Based on sliding mode controller design, a fault tolerant control method is proposed. By means of the feasibility of some linear matrix inequalities (LMIs), delay dependent sufficient condition is derived for the existence of a linear sliding surface which guarantees quadratic stability of the reduced-order equivalent system restricted to the sliding surface. A reaching motion controller, which can...