On -invariant measures and a functional equation
Periodic multiplicative algorithms of Selmer type.
Piecewise convex transformations with no finite invariant measure
Abstract. The paper concerns the problem of the existence of a finite invariant absolutely continuous measure for piecewise -regular and convex transformations T: [0, l]→[0,1]. We show that in the case when T’(0) = 1 and T"(0) exists T does not admit such a measure. This result is complementary to the ones contained in [3] and [5].
Pointwise convergence of nonconventional averages
We answer a question of H. Furstenberg on the pointwise convergence of the averages , where U and R are positive operators. We also study the pointwise convergence of the averages when T and S are measure preserving transformations.
Pointwise Convergence Theorems in L2 over a von Neumann Algebra.
Pointwise ergodic theorems for arithmetic sets
Pointwise ergodic theorems for functions in Lorentz spaces with p ≠ ∞
Let τ be a null preserving point transformation on a finite measure space. Assuming τ is invertible, P. Ortega Salvador has recently obtained sufficient conditions for the almost everywhere convergence of the ergodic averages in with 1 < p < ∞, 1 < q < ∞. In this paper we obtain necessary and sufficient conditions for the almost everywhere convergence, without assuming that τ is invertible and only assuming that p ≠ ∞.
Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations
Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average converges almost everywhere to a function f* in , where (pq) and are assumed to be in the set . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized and unified...
Pointwise induced semigroups of σ-endomorphisms
Pointwise weighted vector ergodic theorem in .
Poisson boundary of triangular matrices in a number field
The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the Poisson boundary of random rational affinities.
Poisson suspensions of compactly regenerative transformations
For infinite measure preserving transformations with a compact regeneration property we establish a central limit theorem for visits to good sets of finite measure by points from Poissonian ensembles. This extends classical results about (noninteracting) infinite particle systems driven by Markov chains to the realm of systems driven by weakly dependent processes generated by certain measure preserving transformations.
Polynômes trigonométriques et marches aléatoires multidimensionnelles : application à la théorie ergodique
Positive Contractions of L2-Spaces.
Positive Lyapunov exponents in families of one dimensional dynamical systems.
Positive measure sets of ergodic rational maps
Power weak mixing does not imply multiple recurrence in infinite measure and other counterexamples.
Power weakly mixing infinite transformations.
Powers of positive polynomials and codings of Markov chains onto Bernoulli shifts.
Precompact contraction of metric uniformities, and the continuity of