Approximations of contraction operators on - I
Approximations of Positive Contractions on Loo. II.
Arithmetic and ergodic properties of 'flipped' continued fraction algorithms
Aspects of uniformity in recurrence
We analyze and cite applications of various, loosely related notions of uniformity inherent to the phenomenon of (multiple) recurrence in ergodic theory. An assortment of results are obtained, among them sharpenings of two theorems due to Bourgain. The first of these, which in the original guarantees existence of sets x,x+h, in subsets E of positive measure in the unit interval, with lower bounds on h depending only on m(E), is expanded to the case of arbitrary finite polynomial configurations...
Asymptotic periodicity of Markov operators on signed measures
A new criterion of asymptotic periodicity of Markov operators on , established in [3], is extended to the class of Markov operators on signed measures.
Asymptotic stability of densities for piecewise convex maps
We study the asymptotic stability of densities for piecewise convex maps with flat bottoms or a neutral fixed point. Our main result is an improvement of Lasota and Yorke's result ([5], Theorem 4).
Attracteurs, orbites et ergodicité
Automate des préfixes-suffixes associé à une substitution primitive
On explicite une conjugaison en mesure entre le décalage sur le système dynamique associé à une substitution primitive et une transformation adique sur le support d'un sous-shift de type fini, à savoir l'ensemble des chemins d'un automate dit des préfixes-suffixes. En caractérisant les préimages par la conjugaison des chemins périodiques de l'automate, on montre que cette conjugaison est injective sauf sur un ensemble dénombrable, sur lequel elle est finie-à-un. On en déduit l'existence d'une suite...
Automorphisms of the algebra of operators in preserving conditioning
Let α be an isometric automorphism of the algebra of bounded linear operators in (p ≥ 1). Then α transforms conditional expectations into conditional expectations if and only if α is induced by a measure preserving isomorphism of [0, 1].
Automorphisms with finite exact uniform rank
The notion of exact uniform rank, EUR, of an automorphism of a probability Lebesgue space is defined. It is shown that each ergodic automorphism with finite EUR is finite extension of some automorphism with rational discrete spectrum. Moreover, for automorphisms with finite EUR, the upper bounds of EUR of their factors and ergodic iterations are computed.
Bands of invariantly extensible measures.
Binomial-Coefficient Multiples of Irrationals.
Borel matrix
We study the Borel summation method. We obtain a general sufficient condition for a given matrix to have the Borel property. We deduce as corollaries, earlier results obtained by G. M“uller and J.D. Hill. Our result is expressed in terms belonging to the theory of Gaussian processes. We show that this result cannot be extended to the study of the Borel summation method on arbitrary dynamical systems. However, in the -setting, we establish necessary conditions of the same kind by using Bourgain’s...
Bounded variation and invariant measures
BV coboundaries over irrational rotations
For every irrational rotation we construct a coboundary which is continuous except at a single point where it has a jump, is nondecreasing, and has zero derivative almost everywhere.
Capacités invariantes extrémales
On étudie certains cônes de mesures sur un espace localement compact, qui sont invariantes par l’action continue d’un groupe localement compact , cette étude étant centrée sur les génératrices extrémales de ces cônes. On dégage d’abord un type très simple d’action continue où l’on décrit complètement la situation. On dégage ensuite une classe d’actions (contenant par exemple l’action de shift de Bernoulli sur ) qui ne sont pas du type précédent, et que l’on étudie en grand détail. Le résultat...
Catching small sets under Flows
Central limit theorems for non-invertible measure preserving maps
Using the Perron-Frobenius operator we establish a new functional central limit theorem for non-invertible measure preserving maps that are not necessarily ergodic. We apply the result to asymptotically periodic transformations and give a specific example using the tent map.
Characterizing mildly mixing actions by orbit equivalence of products.
Classification des automorphismes ergodiques et finitaires