Differential Equations

Ergodic Theory of Expanding Thurston Maps (Atlantis Studies - download pdf or read online

By Zhiqiang Li

Thurston maps are topological generalizations of postcritically-finite rational maps. This ebook presents a finished research of ergodic idea of increasing Thurston maps, targeting the degree of maximal entropy, in addition to a extra common type of invariant measures, known as equilibrium states, and likely vulnerable growth homes of such maps. specifically, we current equidistribution effects for iterated preimages and periodic issues with admire to the original degree of maximal entropy via investigating the quantity and destinations of fastened issues. We then use the thermodynamical formalism to set up the lifestyles, forte, and diverse different houses of the equilibrium country for a Holder non-stop strength at the sphere outfitted with a visible metric. After learning a few vulnerable enlargement homes of such maps, we receive convinced huge deviation rules for iterated preimages and periodic issues less than an extra assumption at the serious orbits of the maps. this allows us to acquire basic equidistribution effects for such issues with admire to the equilibrium states lower than a similar assumption.

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Ergodic Theory of Expanding Thurston Maps (Atlantis Studies in Dynamical Systems) by Zhiqiang Li

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