On C2-Diffeomorphisms of the Circle which are of Type III1.
On disjointness properties of some smooth flows
Special flows over some locally rigid automorphisms and under L² ceiling functions satisfying a local L² Denjoy-Koksma type inequality are considered. Such flows are proved to be disjoint (in the sense of Furstenberg) from mixing flows and (under some stronger assumption) from weakly mixing flows for which the weak closure of the set of all instances consists of indecomposable Markov operators. As applications we prove that ∙ special flows built over ergodic interval exchange...
On extremal and perfect σ-algebras for flows
It is shown that there exists a flow on a Lebesgue space with finite entropy and an extremal σ-algebra of it which is not perfect.
On invariant measures for the tend map.
The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mub for each parameter value b. The continuity of the map b --> mub is established.
On measure-preserving transformations and doubly stationary symmetric stable processes
In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular set isomorphisms...
On metric isomorphism of Morse dynamical systems
On Riemann Sums and Lebesgue Integrals.
On the decomposition of continuous flows on the Polish space
On the existence of an invariant measure for the dynamical system generated by partial differential equation
On the generalization of the Stein-Weiss theorem for the ergodic Hilbert transform
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized to the ergodic Hilbert transform.
On the positivity of an invariant measure on open non-empty sets
On the ratio maximal functions for an ergodic flow
On the sequence of integer parts of a good sequence for the ergodic theorem
If is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts good for the ergodic theorem ? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.
Quasiregular Points and Time Changes.
Random ergodic theorems with universally representative sequences
Rank and spectral multiplicity
For a dynamical system (X,T,μ), we investigate the connections between a metric invariant, the rank r(T), and a spectral invariant, the maximal multiplicity m(T). We build examples of systems for which the pair (m(T),r(T)) takes values (m,m) for any integer m ≥ 1 or (p-1, p) for any prime number p ≥ 3.
Rank is not a spectral invariant
Regular generators for multidimensional dynamical systems
Résolution d'une équation fonctionnelle
Rigid reparametrizations and cohomology for horocycle flows.