Rauzy tilings and bounded remainder sets on the torus.
Razumikhin's method in the qualitative theory of processes with delay.
Reading along arithmetic progressions
Given a 0-1 sequence x in which both letters occur with density 1/2, do there exist arbitrarily long arithmetic progressions along which x reads 010101...? We answer the above negatively by showing that a certain regular triadic Toeplitz sequence does not have this property. On the other hand, we prove that if x is a generalized binary Morse sequence then each block can be read in x along some arithmetic progression.
Real analytic convex surfaces with positive topological entropy and rigid body dynamics.
Real and complex transversely symplectic Anosov flows of dimension five
Nous présentons plusieurs résultats de rigidité concernant les flots d’Anosov admettant transversalement des structures symplectiques réelles ou complexes de dimension .
Real and imaginary parts of polynomial iterates.
Real Koebe principle
We prove a version of the real Koebe principle for interval (or circle) maps with non-flat critical points.
Real commutative differential operators associated with two-dimensional Abelian varieties.
Real Hamiltonian forms of affine Toda models related to exceptional Lie algebras.
Reality conditions of loop solitons genus : hyperelliptic am functions.
Realization of any finite jet in a scalar semilinear parabolic equation on the ball in
Realizing vector fields without loss of derivatives
Recent progress in attractors for quintic wave equations
We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of with damping terms of the form , where or . The main ingredient of the work is the hidden extra regularity of solutions that does not follow from energy estimates. Due to the extra regularity of solutions existence of a smooth attractor then follows from the smoothing property when . For existence of smooth attractors is more complicated and follows...
Recent results in symplectic geometry
Recent results on the separatrix splitting for the standard map
Reconstructing the global dynamics of attractors via the Conley index
Given an unknown attractor 𝓐 in a continuous dynamical system, how can we discover the topology and dynamics of 𝓐? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from 𝓐 onto a model system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 then provides a lower bound for the complexity of 𝓐. The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy for a large...
Reconstruction phases for Hamiltonian systems on cotangent bundles.
Recurrence and mixing recurrence of multiplication operators
Let be a Banach space, the algebra of bounded linear operators on and an admissible Banach ideal of . For , let and denote the left and right multiplication defined by and , respectively. In this paper, we study the transmission of some concepts related to recurrent operators between , and their elementary operators and . In particular, we give necessary and sufficient conditions for and to be sequentially recurrent. Furthermore, we prove that is recurrent if and only...
Récurrence des marches aléatoires et ergodicité du flot géodésique sur les graphes réguliers.
Recurrence of entire transcendental functions with simple post-singular sets
We study how the orbits of the singularities of the inverse of a meromorphic function determine the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero. We concentrate on a family of entire transcendental functions with only finitely many singularities of the inverse, counting multiplicity, all of which either escape exponentially fast or are pre-periodic. For these functions we are able to decide whether the function is recurrent or not. In the case that the Julia set is...