Results 151 to 160 of about 39,038 (168)

Infinite Ergodic Transformations

2014
In the previous chapters we saw that recurrent transformations do not accept wandering sets. An important subset of the recurrent transformations are the ergodic ones that do not have a finite invariant and equivalent measure. These transformations also do not accept wandering sets, yet they must necessarily accept ww and eww sets. For infinite ergodic
Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad   +3 more
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LIPSCHITZ–ERGODIC TRANSFORMATION

Acta Mathematica Scientia, 1988
Abstract In 1977 Eastontt[1] introduced the notion of Lipschitz–ergodic transformation on a compact space. In this paper we consider the Lipschitz–ergodic transformation on a measure space.
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Notes on Ergodic $$2$$-Adic Transformations

p-Adic Numbers, Ultrametric Analysis and Applications, 2020
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Lamperti transformation - Cure for ergodicity breaking

Communications in Nonlinear Science and Numerical Simulation, 2019
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Magdziarz, Marcin, Zorawik, Tomasz
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Mixing Limit Theorems for Ergodic Transformations

Journal of Theoretical Probability, 2007
In this paper, the author firstly proves the following theorem: Let \(R_n\), \(n> 1\), be random variables on the probability space \((X,{\mathcal A}, P)\), taking values in the separable metric space \((M, d)\), and \(R\) a random element of \(M\) such that \(R_n\overset {P}\Rightarrow R\) as \(n\to\infty\). Assume there is a \(\sigma\)-finite measure
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On Ergodic Transformations with Homogeneous Spectrum

Journal of Dynamical and Control Systems, 1999
An old question of Rokhlin asks whether there exists an ergodic automorphism having a homogeneous spectrum of multiplicity two (i.e., the multiplicity function of the induced unitary operator takes the unique value 2, almost everywhere with respect to the maximal spectral type). It was recently shown that if \(A\) is any subset of \(\mathbb{Z}^+\cup \{\
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Jointly ergodic measure-preserving transformations

Israel Journal of Mathematics, 1984
The notion of ergodicity of a measure preserving transformation is generalized to finite sets of transformations. The main result is that, if \(T_ 1,T_ 2,...,T_ s\) are invertible commuting measure preserving transformations, of a probability space (X,\({\mathcal B},\mu)\), then \[ \frac{1}{N-M}\sum^{N-1}_{n=M}T^ n_ 1f_ 1\cdot T^ n_ 2f_ 2\cdot...\cdot ...
Berend, Daniel, Bergelson, Vitaly
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Ergodic transformations in AST

1995
In this article we investigate the ergodicity of set transformations within the Alternative Set Theory. The main result is that each ergodic transformation is homomorhic to the cycle of a suitable length.
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Rigid factors of ergodic transformations

Israel Journal of Mathematics, 1980
We prove a theorem concerning cartesian products of ergodic not necessarily measuring preserving transformations, using the notion of rigid factors for such transformations.
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Characterizations of Measurability-Preserving Ergodic Transformations

Sarajevo Journal of Mathematics
Let ($S, \mathfrak{A}, \mu$) be a finite measure space and let $\phi: S \rightarrow S$ be a transformation which preserves the measure $\mu$. The purpose of this paper is to give some (measure theoretical) necessary and sufficient conditions for the transformation $\phi$ to be measurability-preserving ergodic with respect to $\mu$. The obtained results
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