A01=Daniel Meyer
A01=Mario Bonk
Author_Daniel Meyer
Author_Mario Bonk
Category=PBP
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Product details
- ISBN 9780821875544
- Weight: 1000g
- Dimensions: 178 x 254mm
- Publication Date: 30 Jan 2018
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
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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. A Thurston map 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.
Mario Bonk, University of California, Los Angeles, CA.
Daniel Meyer, University of Liverpool, UK.
Daniel Meyer, University of Liverpool, UK.
