000			02085cam a22002658i 4500
001			138311
003			ISI Library, Kolkata
005			20180511120813.0
008			170412s2017 riu b 001 0 eng
020			_a9780821875544 (alk. paper)
040			_aISI Library
082	0	4	_a510MS _223 _bAm512
100	1		_aBonk, Mario, _eauthor
245	1	0	_aExpanding Thurston maps / _cMario Bonk and Daniel Meyer.
260			_aProvidence : _bAmerican Mathematical Society, _c©2017.
300			_axv, 478 pages : _billustrations ; _c27 cm.
490	0		_aMathematical surveys and monographs ; _vv 225.
504			_aIncludes bibliographical references and index.
505	0		_a1. 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.
520			_aThis 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.
650		0	_aAlgebraic topology.
650		0	_aMappings (Mathematics)
700	1		_aMeyer, Daniel, _eauthor
942			_2ddc _cBK
999			_c424601 _d424601