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Entropy zero area preserving diffeomorphisms of $S^2$

John Franks and Michael Handel

Geometry & Topology 16 (2012) 2187–2284
Bibliography
1 R Bowen, Entropy and the fundamental group, from: "The structure of attractors in dynamical systems" (editors N G Markley, J C Martin, W Perrizo), Lecture Notes in Math. 668, Springer (1978) 21 MR518545
2 M Brown, J M Kister, Invariance of complementary domains of a fixed point set, Proc. Amer. Math. Soc. 91 (1984) 503 MR744656
3 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988) MR964685
4 B Farb, Some problems on mapping class groups and moduli space, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 11 MR2264130
5 A Fathi, F Laudenbach, V Poenaru, Editors, Travaux de Thurston sur les surfaces, Astérisque 66–67, Soc. Math. France (1979) 284 MR568308
6 D Fisher, Groups acting on manifolds: around the Zimmer program, from: "Geometry, rigidity, and group actions" (editors B Farb, D Fisher), Univ. Chicago Press (2011) 72 MR2807830
7 J Franks, Generalizations of the Poincaré–Birkhoff theorem, Ann. of Math. 128 (1988) 139 MR951509
8 J Franks, Recurrence and fixed points of surface homeomorphisms, Ergodic Theory Dynam. Systems 8∗ (1988) 99 MR967632
9 J Franks, Area preserving homeomorphisms of open surfaces of genus zero, New York J. Math. 2 (1996) 1 MR1371312
10 J Franks, Distortion in groups of circle and surface diffeomorphisms, from: "Dynamique des difféomorphismes conservatifs des surfaces: un point de vue topologique", Panor. Synthèses 21, Soc. Math. France (2006) 35 MR2288284
11 J Franks, M Handel, Periodic points of Hamiltonian surface diffeomorphisms, Geom. Topol. 7 (2003) 713 MR2026545
12 J Franks, M Handel, Distortion elements in group actions on surfaces, Duke Math. J. 131 (2006) 441 MR2219247
13 J Franks, M Handel, Global fixed points for centralizers and Morita's theorem, Geom. Topol. 13 (2009) 87 MR2469514
14 M Handel, A pathological area preserving $C^{\infty }$ diffeomorphism of the plane, Proc. Amer. Math. Soc. 86 (1982) 163 MR663889
15 M Handel, The rotation set of a homeomorphism of the annulus is closed, Comm. Math. Phys. 127 (1990) 339 MR1037109
16 M Handel, Commuting homeomorphisms of $S^2$, Topology 31 (1992) 293 MR1167171
17 M Handel, A fixed-point theorem for planar homeomorphisms, Topology 38 (1999) 235 MR1660349
18 M W Hirsch, Differential topology, Graduate Texts in Mathematics 33, Springer (1994) MR1336822
19 N V Ivanov, Fifteen problems about the mapping class groups, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 71 MR2264532
20 A Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Inst. Hautes Études Sci. Publ. Math. (1980) 137 MR573822
21 R Kirby, Problems in low dimensional manifold theory, from: "Algebraic and geometric topology. Part 2." (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 273 MR520548
22 M Korkmaz, Problems on homomorphisms of mapping class groups, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 81 MR2264533
23 J N Mather, Topological proofs of some purely topological consequences of Carathéodory's theory of prime ends, from: "Selected studies: physics-astrophysics, mathematics, history of science" (editors T M Rassias, G M Rassias), North-Holland (1982) 225 MR662863
24 J D McCarthy, On the first cohomology group of cofinite subgroups in surface mapping class groups, Topology 40 (2001) 401 MR1808225
25 L Polterovich, Growth of maps, distortion in groups and symplectic geometry, Invent. Math. 150 (2002) 655 MR1946555
26 C P Simon, A bound for the fixed-point index of an area-preserving map with applications to mechanics, Invent. Math. 26 (1974) 187 MR0353372
27 W P Thurston, A generalization of the Reeb stability theorem, Topology 13 (1974) 347 MR0356087
28 Y Yomdin, Volume growth and entropy, Israel J. Math. 57 (1987) 285 MR889979