By Zhiqiang Li

Thurston maps are topological generalizations of postcritically-finite rational maps. This e-book presents a complete learn of ergodic concept of increasing Thurston maps, targeting the degree of maximal entropy, in addition to a extra common classification of invariant measures, known as equilibrium states, and sure vulnerable growth houses of such maps. specifically, we current equidistribution effects for iterated preimages and periodic issues with admire to the original degree of maximal entropy through investigating the quantity and destinations of mounted issues. We then use the thermodynamical formalism to set up the life, distinctiveness, and diverse different houses of the equilibrium kingdom for a Holder non-stop strength at the sphere outfitted with a visible metric. After learning a few susceptible enlargement homes of such maps, we receive definite 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 common equidistribution effects for such issues with appreciate to the equilibrium states less than a similar assumption.

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