**Mathematical Surveys and Monographs**

Volume: 225;
2017;
478 pp;
Hardcover

MSC: Primary 37; 30;

Print ISBN: 978-0-8218-7554-4

Product Code: SURV/225

List Price: $169.00

Individual Member Price: $135.20

**Electronic ISBN: 978-1-4704-4252-1
Product Code: SURV/225.E**

List Price: $169.00

Individual Member Price: $135.20

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# Expanding Thurston Maps

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*Mario Bonk; Daniel Meyer*

This monograph is devoted to the study of the dynamics of expanding
Thurston maps under iteration. A Thurston map is a branched covering
map on a two-dimensional topological sphere such that each critical
point of the map has a finite orbit under iteration. It is
called expanding if, roughly speaking, preimages of a fine open cover
of the underlying sphere under iterates of the map become finer and
finer as the order of the iterate increases.

Every expanding Thurston map gives rise to a fractal space, called
its visual sphere. Many dynamical properties of the map are encoded in
the geometry of this visual sphere. For example, an expanding Thurston
map is topologically conjugate to a rational map if and only if its
visual sphere is quasisymmetrically equivalent to the Riemann
sphere. This relation between dynamics and fractal geometry is the
main focus for the investigations in this work.

The book is an introduction to the subject. The prerequisites for
the reader are modest and include some basic knowledge of complex
analysis and topology. The book has an extensive appendix, where
background material is reviewed such as orbifolds and branched
covering maps.

#### Readership

Graduate students and researchers interested in dynamical systems and topological dynamics.