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Displaying 361 – 380 of 601

On the distribution function of the majorant of ergodic means

Lasha Epremidze (1992)

Studia Mathematica

Let T be a measure-preserving ergodic transformation of a measure space (X,,μ) and, for f ∈ L(X), let $f * = s u p_{N} 1 / N \sum_{m = 0}^{N - 1} f \circ T^{m}$ . In this paper we mainly investigate the question of whether (i) $ʃ_{a}^{\infty} | μ (f * > t) - 1 / t ʃ_{(f * > t)} f d μ | d t < \infty$ and whether (ii) $ʃ_{a}^{\infty} | μ (f * > t) - 1 / t ʃ_{(f > t)} f d μ | d t < \infty$ for some a > 0. It is proved that (i) holds for every f ≥ 0. (ii) holds if f ≥ 0 and f log log (f + 3) ∈ L(X) or if μ(X) = 1 and the random variables $f \circ T^{m}$ are independent. Related inequalities are proved. Some examples and counterexamples are constructed. Several known results are obtained as corollaries.

On the Distribution of Periodic Points for ß-Shifts.

Karl Sigmund (1976)

Monatshefte für Mathematik

On the ergodic decomposition for a cocycle

Jean-Pierre Conze, Albert Raugi (2009)

Colloquium Mathematicae

Let (X,,μ,τ) be an ergodic dynamical system and φ be a measurable map from X to a locally compact second countable group G with left Haar measure $m_{G}$ . We consider the map $τ_{φ}$ defined on X × G by $τ_{φ} : (x, g) \mapsto (τ x, φ (x) g)$ and the cocycle ${(φ ₙ)}_{n \in ℤ}$ generated by φ. Using a characterization of the ergodic invariant measures for $τ_{φ}$ , we give the form of the ergodic decomposition of $μ (d x) \otimes m_{G} (d g)$ or more generally of the $τ_{φ}$ -invariant measures $μ_{χ} (d x) \otimes χ (g) m_{G} (d g)$ , where $μ_{χ} (d x)$ is χ∘φ-conformal for an exponential χ on G.

On the existence of finite generators for invertible measure-preserving transformations

Karel Winkelbauer (1977)

Commentationes Mathematicae Universitatis Carolinae

On the existence of invariant measures for piecewise convex transformations

P. Kasprowski (1983)

Annales Polonici Mathematici

On the generalization of the Stein-Weiss theorem for the ergodic Hilbert transform

Lasha Ephremidze (2003)

Studia Mathematica

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 generalized Avez method

Antoni Leon Dawidowicz (1992)

Annales Polonici Mathematici

A generalization of the Avez method of construction of an invariant measure is presented.

On the growth of averaged Weyl sums for rigid rotations

S. de Bièvre, G. Forni (1998)

Studia Mathematica

On the individual ergodic theorem for subsequences

Ryotaro Sato (1973)

Studia Mathematica

On the Infinite Product Construction of Non-Singular Transformations of a Measure Space.

Wolfgang Krieger (1971/1972)

Inventiones mathematicae

On the integrability of the ergodic Hilbert transform for a class of functions with equal absolute values.

Ephremidze, L. (1998)

Georgian Mathematical Journal

On the integrability of the ergodic maximal function

Burgess Davis (1982)

Studia Mathematica

On the invariance principle for non-uniformly expanding transformations of [0, 1].

Massimo Campanino, Stefano Isola (1996)

Forum mathematicum

On the invariant measure for Jacobi-Perron algorithm.

Schweiger, F. (1990)

Mathematica Pannonica

On the lifting of invariant measures

Antoni Leon Dawidowicz (1990)

Annales Polonici Mathematici

On the local ergodic theorems of Krengel, Kubokawa, and Terrell

S. A. McGrath (1976)

Commentationes Mathematicae Universitatis Carolinae

On the multiplicity function of ergodic group extensions, II

Jakub Kwiatkowski, Mariusz Lemańczyk (1995)

Studia Mathematica

For an arbitrary set $A \subseteq ℕ^{+}$ containing 1, an ergodic automorphism T whose set of essential values of the multiplicity function is equal to A is constructed. If A is additionally finite, T can be chosen to be an analytic diffeomorphism on a finite-dimensional torus.

On the multiplicity function of ergodic group extensions of rotations

G. Goodson, J. Kwiatkowski, M. Lemańczyk, P. Liardet (1992)

Studia Mathematica

For an arbitrary set A ⊆ ℕ satisfying 1 ∈ A and lcm(m₁,m₂) ∈ A whenever m₁,m₂ ∈ A, an ergodic abelian group extension of a rotation for which the range of the multiplicity function equals A is constructed.

On the pointwise dimension of hyperbolic measures: a proof of the Eckmann-Ruelle conjecture.

Barreira, Luis, Pesin, Yakov, Schmeling, Jörg (1996)

Electronic Research Announcements of the American Mathematical Society [electronic only]

On the Pointwise Ergodic Theorem in $L_{p}$

F. Martín-Reyes, A. de la Torre (1994)

Studia Mathematica

Currently displaying 361 – 380 of 601

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