Displaying similar documents to “Most expanding maps have no absolutely continuous invariant measure”

Invariant densities for C¹ maps

Anthony Quas (1996)

Studia Mathematica

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We consider the set of C 1 expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of C 1 expanding maps with the C 1 topology. This is in contrast with results for C 2 or C 1 + ε maps, where the invariant densities can be shown to be continuous.

Completely mixing maps without limit measure

Gerhard Keller (2004)

Colloquium Mathematicae

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We combine some results from the literature to give examples of completely mixing interval maps without limit measure.

The uniqueness of Haar measure and set theory

Piotr Zakrzewski (1997)

Colloquium Mathematicae

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Let G be a group of homeomorphisms of a nondiscrete, locally compact, σ-compact topological space X and suppose that a Haar measure on X exists: a regular Borel measure μ, positive on nonempty open sets, finite on compact sets and invariant under the homeomorphisms from G. Under some mild assumptions on G and X we prove that the measure completion of μ is the unique, up to a constant factor, nonzero, σ-finite, G-invariant measure defined on its domain iff μ is ergodic and the G-orbits...

Invariant extension of Haar measure

Antal Járai

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CONTENTS§1. Introduction...............................................................5§2. Covariant extension of measures..............................6§3. An invariant extension of Haar measure..................15§4. Covariant extension of Lebesgue measure.............22References....................................................................26

Asymptotic stability of densities for piecewise convex maps

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).