Selections and their absolutely continuous invariant measures
نویسندگان
چکیده
منابع مشابه
Absolutely Continuous Invariant Measures That Are Maximal
Let A be a certain irreducible 0-1 matrix and let t denote the family of piecewise linear Markov maps on [0,1] which are consistent with A. The main result of this paper characterizes those maps in t whose (unique) absolutely continuous invariant measure is maximal, and proves that for "most" of the maps that are consistent with A, the absolutely continuous invariant measure is not maximal.
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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. Introduction Let (X,B, m, T ) be an invertible, ergodic measure preserving transformation of a σ-finite measure space, then there are no other σ-finite, m-absolu...
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In the current paper we study in more detail some properties of the absolutely continuous invariant measures constructed in the course of the proof of Jakobson's Theorem. In particular, we show that the density of the invariant measure is continuous at Misiurewicz points. From this we deduce that the Lyapunov exponent is also continuous at these points (our considerations apply just to the para...
متن کاملA Generalization of Straube’s Theorem: Existence of Absolutely Continuous Invariant Measures for Random Maps
A randommap is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied at each iteration of the process. In this paper, we study randommaps. The main result provides a necessary and sufficient condition for the existence of absolutely continuous invariant measure for a randommap with constant probabilities and position-dependent probabilities.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2014
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.11.043