Convergence of discretized attractors for parabolic equations on the line.
Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains
We present a spectral theory for a class of operators satisfying a weak “Doeblin–Fortet” condition and apply it to a class of transition operators. This gives the convergence of the series , , under some regularity assumptions and implies the central limit theorem with a rate in for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.
Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains
We present a spectral theory for a class of operators satisfying a weak “Doeblin–Fortet" condition and apply it to a class of transition operators. This gives the convergence of the series ∑k≥0krPkƒ, , under some regularity assumptions and implies the central limit theorem with a rate in for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.
Convergence of multiple ergodic averages along cubes for several commuting transformations
We prove the norm convergence of multiple ergodic averages along cubes for several commuting transformations, and derive corresponding combinatorial results. The method we use relies primarily on the "magic extension" established recently by B. Host.
Convergence of nonautonomous evolutionary algorithm.
Convergence of pinching deformations and matings of geometrically finite polynomials
We give a thorough study of Cui's control of distortion technique in the analysis of convergence of simple pinching deformations, and extend his result from geometrically finite rational maps to some subset of geometrically infinite maps. We then combine this with mating techniques for pairs of polynomials to establish existence and continuity results for matings of polynomials with parabolic points. Consequently, if two hyperbolic quadratic polynomials tend to their respective root polynomials...
Convergence Rates of the POD–Greedy Method
Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a priori convergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy...
Convergence results for periodic solutions of nonautonomous Hamiltonian systems
We prove some stability results for a certain class of periodic solutions of nonautonomous Hamiltonian systems in the case of Hamiltonian functions either with subquadratic growth or homogeneous with superquadratic growth. Thus we extend to the nonautonomous case some results recently established by the Authors for the autonomous case.
Convex billiards and a theorem by E. Hops.
Convexes divisibles III
Convexity Properties of the Moment Mapping.
Convexity properties of the moment mapping. II.
Convexity properties of the moment mapping. III.
Coproducts and the additivity of the Szymczak index
We prove that the index defined by Szymczak in [9] has an additivity property. Moreover we give an abstract theorem for extending coproducts from an initial category to the Szymczak category, which provides a setting for the proof of additivity.
Correction to: Connecting invariant manifolds and the solution of the stability and -stability conjectures for flows.
Correction to “Properties of pseudoholomorphic curves in symplectisations. I : asymptotics”
Correction to the paper "Divergent trajectories of flows on homogeneous spaces and Diophantine approximations".
Corrections to "L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper triangular matrices" (Fund. Math. 156 (1998), 99–110)
Correlation asymptotics from large deviations in dynamical systems with infinite measure
We extend a result of Doney [Probab. Theory Related Fields 107 (1997)] on renewal sequences with infinite mean to renewal sequences of operators. As a consequence, we get precise asymptotics for the transfer operator and for correlations in dynamical systems preserving an infinite measure (including intermittent maps with an arbitrarily neutral fixed point).
Correlation dimension for self-similar Cantor sets with overlaps
We prove a classification theorem of the “Glimm-Effros” type for Borel order relations: a Borel partial order on the reals either is Borel linearizable or includes a copy of a certain Borel partial order which is not Borel linearizable.