Good Banach spaces for piecewise hyperbolic maps via interpolation
A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.
The main aim of this paper is to give some counterexamples to global invertibility of local diffeomorphisms which are interesting in mechanics. The first is a locally strictly convex function whose gradient is non-injective. The interest in this function is related to the Legendre transform. Then I show two non-injective canonical local diffeomorphisms which are rational: the first is very simple and related to the complex cube, the second is defined on the whole ℝ⁴ and is obtained from a recent...
We consider positional numeration systems with negative real base , where , and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal -representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the positive base with a non-integer alphabet. This enables us to characterize digit sequences admissible as greedy...
Combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis we introduce a new method for spectral analysis on self-similar graphs.First, for a rather general, axiomatically defined class of self-similar graphs a graph theoretic analogue to the Banach fixed point theorem is proved. The subsequent results hold for a subclass consisting of “symmetrically” self-similar graphs which however is still more general then...
We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group -action has been considered on a strongly monotone skew-product semiflow. Here we relax the strong monotonicity and compactness requirements, and establish a theory concerning symmetry or monotonicity properties of uniformly stable 1-cover minimal sets. We then apply this theory to show rotational symmetry of certain stable entire solutions for a class of...
Soient un espace symétrique de type non compact et un groupe discret d’isométries de du type de Schottky. Dans cet article, nous donnons des équivalents des fonctions orbitales de comptage pour l’action de sur .
The purpose of this paper is to prove the existence of a symplectic realization for a large class of regular Poisson manifolds with Riemannian two dimensional characteristic foliation. To do so, we will show that the homotopy groupoid of a Riemannian foliation is locally trivial.
We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the -topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic subgroup of finite index or a nonabelian free subgroup.