A mixing dynamical system on the Cantor set.
Kim, Jeong H. (1995)
International Journal of Mathematics and Mathematical Sciences
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Kim, Jeong H. (1995)
International Journal of Mathematics and Mathematical Sciences
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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.
Zbigniew Kowalski (1987)
Studia Mathematica
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Ulrich Krengel (1976)
Annales de l'I.H.P. Probabilités et statistiques
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Krzysztof Frączek (2000)
Colloquium Mathematicae
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We consider measure-preserving diffeomorphisms of the torus with zero entropy. We prove that every ergodic -diffeomorphism with linear growth of the derivative is algebraically conjugate to a skew product of an irrational rotation on the circle and a circle -cocycle. We also show that for no positive β ≠ 1 does there exist an ergodic -diffeomorphism whose derivative has polynomial growth with degree β.
Maximilian Thaler (2000)
Studia Mathematica
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We determine the asymptotic behaviour of the iterates of the Perron-Frobenius operator for specific interval maps with an indifferent fixed point which gives rise to an infinite invariant measure.
thomas Hoover, Alan Lambert, Joseph Quinn (1982)
Studia Mathematica
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Thomas Bogenschütz, Zbigniew Kowalski (1996)
Studia Mathematica
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We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.