Invariant measures and ergodic properties of number theoretical endomorphisms
F. Schweiger (1989)
Banach Center Publications
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F. Schweiger (1989)
Banach Center Publications
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Adl-Zarabi, Kourosh, Proppe, Harald (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Francesc Bofill (1988)
Stochastica
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The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mu for each parameter value b. The continuity of the map b --> mu is established.
P. Kasprowski (1983)
Annales Polonici Mathematici
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M. Jabłoński (1976)
Annales Polonici Mathematici
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Giulio Pianigiani (1981)
Annales Polonici Mathematici
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Franz Hofbauer, Gerhard Keller (1982)
Mathematische Zeitschrift
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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.
B. Schmitt (1989)
Banach Center Publications
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Alexander I. Bufetov (2014)
Annales de l’institut Fourier
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The main result of this note, Theorem 1.3, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant and ergodic under the action of the infinite unitary group and that admits well-defined projections onto the quotient space of “corners" of finite size, must be finite. A similar result, Theorem 1.1, is also established for unitarily invariant measures on the space of all infinite complex matrices. These results imply that the infinite Hua-Pickrell...
Antoni Leon Dawidowicz (1990)
Annales Polonici Mathematici
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Tomoki Inoue (1992)
Annales Polonici Mathematici
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We study the asymptotic stability of densities for piecewise convex maps with flat bottoms or a neutral fixed point. Our main result is an improvement of Lasota and Yorke's result ([5], Theorem 4).
Anthony Quas (1999)
Studia Mathematica
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We consider the topological category of various subsets of the set of expanding maps from a manifold to itself, and show in particular that a generic expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for or expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.
Piotr Bugiel (1996)
Mathematische Zeitschrift
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S. G. Dani, M. Keane (1979)
Annales de l'I.H.P. Probabilités et statistiques
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