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Expanding in the Mean

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2036)

Abstract

In this chapter we show that the main achievements of this manuscript, including thermodynamical formalism, Bowen’s formula and multifractal analysis, also hold for a class of random maps satisfying an allegedly weaker expanding condition

$$\int \nolimits \nolimits \log {\gamma }_{x}\mathit{dm}(x) > 0.$$

We start with a precise definition of this class. Then we explain how this case can be reduced to random expanding maps by looking at an appropriate induced map. The picture is completed by providing and discussing a concrete map that is not expanding but expanding in the mean.

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Correspondence to Volker Mayer .

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© 2011 Springer-Verlag Berlin Heidelberg

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Mayer, V., Skorulski, B., Urbanski, M. (2011). Expanding in the Mean. In: Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry. Lecture Notes in Mathematics(), vol 2036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23650-1_7

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