Ergodic Theory of Expanding Thurston Maps is popular PDF and ePub book, written by Zhiqiang Li in 2017-04-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Ergodic Theory of Expanding Thurston Maps can be Read Online from any device for your convenience.
Ergodic Theory of Expanding Thurston Maps Book PDF Summary
Thurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of such maps. In particular, we present equidistribution results for iterated preimages and periodic points with respect to the unique measure of maximal entropy by investigating the number and locations of fixed points. We then use the thermodynamical formalism to establish the existence, uniqueness, and various other properties of the equilibrium state for a Holder continuous potential on the sphere equipped with a visual metric. After studying some weak expansion properties of such maps, we obtain certain large deviation principles for iterated preimages and periodic points under an additional assumption on the critical orbits of the maps. This enables us to obtain general equidistribution results for such points with respect to the equilibrium states under the same assumption.
Detail Book of Ergodic Theory of Expanding Thurston Maps PDF
- Author : Zhiqiang Li
- Release : 06 April 2017
- Publisher : Springer
- ISBN : 9789462391741
- Genre : Mathematics
- Total Page : 190 pages
- Language : English
- PDF File Size : 21,8 Mb
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