Conservation laws of discrete Korteweg-de Vries equation.
We obtain conditions for L₂ and strong consistency of the least square estimators of the coefficients in a multi-linear regression model with a stationary random noise. For given non-random regressors, we obtain conditions which ensure L₂-consistency for all wide sense stationary noise sequences with spectral measure in a given class. The condition for the class of all noises with continuous (i.e., atomless) spectral measures yields also -consistency when the noise is strict sense stationary with...
A mathematical model based on the principle of less contractions is proposed for the construction of velocity vector fields and forces from given integrals. Necessary algebraic conditions for the solution of the problem are deduced. In addition, the velocity vector field is extended in a neighbourhood of the integrals. Applications and examples are given.
We show that if is a discrete subgroup of the group of the isometries of , and if is a representation of into the group of the isometries of , then any -equivariant map extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Then, we show that the weak extension we obtain is actually a measurable -equivariant...
Étant donné un automorphisme d’un groupe libre et un représentant topologique train-track de son inverse, on peut construire un arbre réel appelé arbre répulsif de . Le groupe libre agit sur par isométries. La dynamique engendrée par peut être représentée par l’action du groupe libre restreinte à un sous-ensemble compact bien choisi du complété métrique de . Cet article construit ce sous-ensemble sur une classe d’exemples en introduisant des opérations appelées substitutions d’arbre ;...
We elaborate a method allowing the determination of 0-1 matrices corresponding to dynamics of the interval having stable, 2k-periodic orbits, k belonging to N. By recurrence on the finite dimensional matrices, we establish the form of the infinite matrices (k --> ∞).
This paper is a study of the global structure of the attractors of a dynamical system. The dynamical system is associated with an oriented graph called a Symbolic Image of the system. The symbolic image can be considered as a finite discrete approximation of the dynamical system flow. Investigation of the symbolic image provides an opportunity to localize the attractors of the system and to estimate their domains of attraction. A special sequence of symbolic images is considered in order to obtain...
We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on the "closure...