Displaying similar documents to “Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents”

Most expanding maps have no absolutely continuous invariant measure

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 C 1 expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for C 2 or C 1 + ε expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.

Linear growth of the derivative for measure-preserving diffeomorphisms

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 C 1 -diffeomorphism with linear growth of the derivative is algebraically conjugate to a skew product of an irrational rotation on the circle and a circle C 1 -cocycle. We also show that for no positive β ≠ 1 does there exist an ergodic C 2 -diffeomorphism whose derivative has polynomial growth with degree β.

Exactness of skew products with expanding fibre maps

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.