Factors and Extensions of Full Shifts.
Factors of coalescent automorphisms
Factors of ergodic group extensions of rotations
Diagonal metric subgroups of the metric centralizer of group extensions are investigated. Any diagonal compact subgroup Z of is determined by a compact subgroup Y of a given metric compact abelian group X, by a family , of group automorphisms and by a measurable function f:X → G (G a metric compact abelian group). The group Z consists of the triples , y ∈ Y, where , x ∈ X.
Faithful zero-dimensional principal extensions
We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν | X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the authors' result in Acta Appl. Math. [to appear] (where the extension was principal, but not necessarily faithful).
Fibrés dynamiques. Entropie et dimension
Finitarily Bernoulli factors are dense
It is not known if every finitary factor of a Bernoulli scheme is finitarily isomorphic to a Bernoulli scheme (is finitarily Bernoulli). In this paper, for any Bernoulli scheme X, we define a metric on the finitary factor maps from X. We show that for any finitary map f: X → Y, there exists a sequence of finitary maps fₙ: X → Y(n) that converges to f, where each Y(n) is finitarily Bernoulli. Thus, the maps to finitarily Bernoulli factors are dense. Let (X(n)) be a sequence of Bernoulli schemes such...
Finitary orbit equivalence and measured Bratteli diagrams
We prove a strengthened version of Dye's theorem on orbit equivalence, showing that if the transformation structures are represented as finite coordinate change equivalence relations of ergodic measured Bratteli diagrams, then there is a finitary orbit equivalence between these diagrams.
Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
We construct a map on the space of interval exchange transformations, which generalizes the classical map on the interval, related to continued fraction expansion. This map is based on Rauzy induction, but unlike its relative kown up to now, the map is ergodic with respect to some finite absolutely continuous measure on the space of interval exchange transformations. We present the prescription for calculation of this measure based on technique developed by W. Veech for Rauzy induction.We study...
Finite generators of ergodic endomorphisms
Finite Procedures for Sofic Systems.
Finite rank actions and the loosely Bernoulli property.
Finite rank transformation and weak closure theorem
Finite return times for measure-preserving transformations.
Finiteness of Ergodic Unitarily Invariant Measures on Spaces of Infinite Matrices
The main result of this note, Theorem 1.3, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant and ergodic under the action of the infinite unitary group and that admits well-defined projections onto the quotient space of “corners" of finite size, must be finite. A similar result, Theorem 1.1, is also established for unitarily invariant measures on the space of all infinite complex matrices. These results imply that the infinite Hua-Pickrell measures...
Fixed points of measure preserving torus homeomorphisms.
Fixed points of semigroups of positive operators in KB-spaces
Flow equivalence, hyperbolic systems and a new zeta function for flows.
Flux moyen d'un courant électrique dans un réseau aléatoire stationnaire de résistances
For almost every tent map, the turning point is typical
Let be the tent map with slope a. Let c be its turning point, and the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, . As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.
Formule(s) de Pesin