On the Pointwise Ergodic Behaviour of Transformations Preserving Infinite Measures
Jon Aaronson (1977)
Publications mathématiques et informatique de Rennes
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Jon Aaronson (1977)
Publications mathématiques et informatique de Rennes
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F. Schweiger (1989)
Banach Center Publications
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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.
Krishna B. Athreya, Peter Ney (1982)
Mathematische Zeitschrift
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Christoph Kopf (1977)
Mathematische Zeitschrift
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F. Hofbauer (1977)
Mathematische Zeitschrift
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John Coffey (1988)
Mathematische Zeitschrift
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Christopher Bose, Véronique Maume-Deschamps, Bernard Schmitt, S. Sujin Shin (2002)
Studia Mathematica
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We investigate the existence and ergodic properties of absolutely continuous invariant measures for a class of piecewise monotone and convex self-maps of the unit interval. Our assumption entails a type of average convexity which strictly generalizes the case of individual branches being convex, as investigated by Lasota and Yorke (1982). Along with existence, we identify tractable conditions for the invariant measure to be unique and such that the system has exponential decay of correlations...
Georges Hansel (1973/74)
Mathematische Zeitschrift
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Zbigniew Kowalski (1994)
Applicationes Mathematicae
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We consider the skew product transformation T(x,y)= (f(x), ) where f is an endomorphism of a Lebesgue space (X,A,p), e : X → S and is a family of Lasota-Yorke type maps of the unit interval into itself. We obtain conditions under which the ergodic properties of f imply the same properties for T. Consequently, we get the asymptotical stability of random perturbations of a single Lasota-Yorke type map. We apply this to some probabilistic model of the motion of cogged bits in the rotary...
Massimo Campanino, Stefano Isola (1996)
Forum mathematicum
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Wolfgang Krieger (1968)
Mathematische Zeitschrift
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Paweł J. Mitkowski, Wojciech Mitkowski (2012)
International Journal of Applied Mathematics and Computer Science
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We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor...
Ryotaro Sato (1994)
Publicacions Matemàtiques
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Let Ti (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 ∈ Lp(μ) the averages Anf(x) = (n + 1)-d Σ0≤ni≤n f(T1 n1 T2 n2...