TY  - BOOK
AU  - Bonk,Mario
AU  - Meyer,Daniel
TI  - Expanding Thurston maps
T2  - Mathematical surveys and monographs
SN  - 9780821875544 (alk. paper)
U1  - 510MS 23
PY  - 2017///
CY  - Providence : 
PB  - American Mathematical Society
KW  - Algebraic topology
KW  - Mappings (Mathematics)
N1  - Includes bibliographical references and index; 1. Introduction --
2. Thurston maps --
3. Lattes maps --
4. Quasiconformal and rough geometry --
5. Cell decompositions --
6.Expansion --
7. Thurston maps with two or three postcritical points --
8. Visual metrics --
9. Symbolic dynamics --
10. Tile graphs --
11. Isotopies --
12. Subdivisions --
13. Quotients of Thurston maps --
14. Combinatorially expanding Thurston maps --
15. Invariant curves --
16. The combinatorial expansion factor --
17. The measure of maximal entropy --
18. The geometry of the visual sphere --
19. Rational Thurston maps and Lebesgue measure --
20. A combinatorial characterization of Lattes maps --
21. Outlook and open problems --
Appendix A --
Bibliography --
Index.
N2  - 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
ER  -