Representation of non-Hamiltonian vector fields in the coordinates of the observer via the isosymplectic geometry.
Représentation par automate de fonctions continues de tore
Soient et un sous-système. est une représentation en base d’une fonction du tore si pour tout point du tore, ses développements en base sont liés par le couplage aux développements en base de . On prouve que si est représentable en base alors , où . Réciproquement, toutes les fonctions de ce type sont représentables en base par un transducteur. On montre finalement que les fonctions du tore qui peuvent être représentées par automate cellulaire sont exclusivement les multiplications...
Representation theorem for stochastic differential equations in Hilbert spaces and its applications.
Representation theory of finite Abelian groups applied to a linear diatomic crystal.
Representations of the Whitehead manifold and Julia sets
Representing real numbers in Möbius number systems
Rescaling of Markov shifts.
Residuality of dynamical morphisms
We present a unified approach to the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein. We show that in a suitable space of measures those measures which define isomorphisms or respectively homomorphisms form residual subsets.
Resolvent conditions and powers of operators
We discuss the relation between the growth of the resolvent near the unit circle and bounds for the powers of the operator. Resolvent conditions like those of Ritt and Kreiss are combined with growth conditions measuring the resolvent as a meromorphic function.
Resonant normal form for even periodic FPU chains
Restricted flows and the soliton equation with self-consistent sources.
Resultados de F. Cano sobre una conjetura de Thom.
Results and open questions on some invariants measuring the dynamical complexity of a map
Let f be a continuous map on a compact connected Riemannian manifold M. There are several ways to measure the dynamical complexity of f and we discuss some of them. This survey contains some results and open questions about relationships between the topological entropy of f, the volume growth of f, the rate of growth of periodic points of f, some invariants related to exterior powers of the derivative of f, and several invariants measuring the topological complexity of f: the degree (for the case...
Resurgence in a Hamilton-Jacobi equation
We study the resurgent structure associated with a Hamilton-Jacobi equation. This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching. We derive the Bridge equation, which encompasses infinitely many resurgent relations satisfied by the formal solution and the other components of the formal integral.
Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé
Henri Poincaré avait déjà remarqué que les variétés stable et instable du pendule perturbé, défini par l’hamiltonienne coïncident pas lorsque que le paramètre n’est pas nul, mais qu’on peut leur associer un même développement formel divergent en puissance de . Cette divergence est ici analysée au moyen de la récente théorie de la résurgence, et du calcul étranger qui permet de trouver un équivalent asymptotique de l’écart des deux variétés pour tendant vers zéro - du moins cela est-il montré...
Retracts, fixed point index and differential equations.
Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions.
Return time statistics for unimodal maps
We prove that a non-flat S-unimodal map satisfying a weak summability condition has exponential return time statistics on intervals around a.e. point. Moreover we prove that the convergence to the entropy in the Ornstein-Weiss formula enjoys normal fluctuations.
Reversibility in the diffeomorphism group of the real line.
Reversible Anosov diffeomorphisms and large deviations.
Reversible complex Hénon maps.