Divergent sequences satisfying the linear fractional transformations.

Mercer, A.McD.

Displaying similar documents to “Divergent sequences satisfying the linear fractional transformations.”

On a pointwise ergodic theorem for multiparameter semigroups.

Ryotaro Sato (1994)

Publicacions Matemàtiques

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Let T_i (i = 1, 2, ..., d) be commuting null preserving transformations on a finite measure space (X, F, μ) and let 1 ≤ p < ∞. In this paper we prove that for every f ∈ L_p(μ) the averages A_nf(x) = (n + 1)^-d Σ_{0≤n_i≤n} f(T₁ ^n₁T₂ ^n_2...

Absolutely continuous, invariant measures for dissipative, ergodic transformations

Jon Aaronson, Tom Meyerovitch (2008)

Colloquium Mathematicae

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We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.

On the ergodic theorems (I) (Generalized ergodic theorems)

C. Ryll-Nardzewski (1951)

Studia Mathematica

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An equivalent measure for some nonsingular transformations and application

I. Assam, J. Woś (1990)

Studia Mathematica

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A mixing dynamical system on the Cantor set.

Kim, Jeong H. (1995)

International Journal of Mathematics and Mathematical Sciences

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Power weak mixing does not imply multiple recurrence in infinite measure and other counterexamples.

Gruher, Kate, Hines, Fred, Patel, Deepam, Silva, Cesar E., Waelder, Robert (2003)

The New York Journal of Mathematics [electronic only]

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A joint limit theorem for compactly regenerative ergodic transformations

David Kocheim, Roland Zweimüller (2011)

Studia Mathematica

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We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zₙ,Sₙ), where Zₙ and Sₙ are respectively the time of the last visit before time n to, and the occupation time of, a suitable set Y of finite measure.

Counting and convergence in ergodic theory

Idris Assani, Zoltán Buczolich, Daniel R. Mauldin (2004)

Acta Universitatis Carolinae. Mathematica et Physica

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Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations

Ryotaro Sato (1995)

Studia Mathematica

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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 $n^{- 1} \sum_{i = 0}^{n - 1} f \circ τ^{i} (x)$ converges almost everywhere to a function f* in $L (p_{1}, q_{1}]$ , where (pq) and $(p_{1}, q_{1}]$ are assumed to be in the set $(r, s) : r = s = 1, o r 1 < r < \infty a n d 1 \leq s \leq \infty, o r r = s = \infty$ . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...

On the ergodic theorems (II) (Ergodic theory of continued fractions)

C. Ryll-Nardzewski (1951)

Studia Mathematica

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Multiparameter pointwise ergodic theorems for Markov operators on L.

Ryotaro Sato (1994)

Publicacions Matemàtiques

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Let P₁, ..., P_d be commuting Markov operators on L_∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each P_i is either conservative or invertible, we prove that for every f in L_p(X,F,μ) with 1 ≤ p < ∞ the averages A_nf = (n + 1)^-d Σ_{0≤n_i≤n} P₁

On μ-compatible metrics and measurable sensitivity

Ilya Grigoriev, Marius Cătălin Iordan, Amos Lubin, Nathaniel Ince, Cesar E. Silva (2012)

Colloquium Mathematicae

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We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure-theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise sensitivity with respect to a large class of metrics. We show that nonsingular ergodic and conservative dynamical systems on standard spaces must be either W-measurably sensitive, or isomorphic mod 0 to a minimal uniformly rigid isometry. In the finite measure-preserving...