Essential dynamics for Lorenz maps on the real line and the lexicographical world
Estimates for Principal Lyapunov Exponents: A Survey
This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....
Étude d’une transformation non uniformément hyperbolique de l’intervalle
Nous étudions un exemple de transformation non uniformément hyperbolique de l’intervalle . Des exemples analogues ont été étudiés par de nombreux auteurs. Notre méthode utilise une théorie spectrale, pour une classe d’opérateurs vérifiant des conditions faibles de Doeblin-Fortet, introduite dans [1]. Elle nous permet, en particulier, de donner une estimation de la vitesse de décroissance des corrélations pour des fonctions non höldériennes.
Eventually periodic points of infra-nil endomorphisms.
Existence criterions for generalized solutions of functional boundary value problems without growth restrictions
Existence et non existence de tores invariants par des difféomorphismes symplectiques
Existence of foliations of Euclidean spaces with all leaves compact.
Existence of homoclinic orbit for second-order nonlinear difference equation.
Existence of homoclinic solutions for a class of nonlinear difference equations.
Existence of unique SRB-measures is typical for real unicritical polynomial families
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows
Existence, persistence and structure of integral manifolds in the neighbourhood of a periodic solution of autonomous differential systems
Existence theorems for commutative diagrams.
Expanding attractors
Expanding maps on Cantor sets and analytic continuation of zeta functions
Expansion growth of foliations
Exponential limit shadowing
We introduce the notion of exponential limit shadowing and show that it is a persistent property near a hyperbolic set of a dynamical system. We show that Ω-stability implies the exponential limit shadowing property.
Extended dynamical systems.
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]....
Factorisation of Lefschetz zeta functions and twisted periodic orbits.