Journal of Modern Dynamics (JMD)

Some virtually abelian subgroups of the group of analytic symplectic diffeomorphisms of a surface
Pages: 369 - 394, Issue 3, September 2013

doi:10.3934/jmd.2013.7.369      Abstract        References        Full text (278.0K)           Related Articles

John Franks - Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, United States (email)
Michael Handel - Department of Mathematics and Computer Science, Lehman College, Bronx, NY 10468, United States (email)

1 M. Artin, Algebra, Prentice Hall, Inc., Englewood Cliffs, NJ, 1991.       
2 M. Bestvina, M. Feighn and M. Handel, The Tits alternative for Out($F^n$). I. Dynamics of exponentially-growing automorphisms, Ann. of Math. (2), 151 (2000), 517-623.       
3 M. Bestvina, M. Feighn and M. Handel, The Tits alternative for Out($F^n$). II. A Kolchin type theorem, Ann. of Math. (2), 161 (2005), 1-59.       
4 E. Bierstone and P. D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math., 67 (1988), 5-42.       
5 M. Brown and J. M. Kister, Invariance of complementary domains of a fixed point set, Proc. Amer. Math. Soc., 91 (1984), 503-504.       
6 B. Farb and P. Shalen, Groups of real-analytic diffeomorphisms of the circle, Ergodic Theory Dynam. Systems, 22 (2002), 835-844.       
7 J. Franks and M. Handel, Entropy zero area preserving diffeomorphisms of $S^2$, Geometry & Topology, 16 (2012), 2187-2284.       
8 J. Franks, Generalizations of the Poincaré-Birkhoff Theorem, Ann. of Math. (2), 128 (1988), 139-151.       
9 J. Franks, Recurrence and fixed points of surface homeomorphisms, Ergodic Theory Dynam. Systems, 8$^*$ (1988), 99-107.       
10 N. V. Ivanov, Subgroups of Teichmüller Modular Groups, Translated from the Russian by E. J. F. Primrose and revised by the author, Translations of Mathematical Monographs, 115, American Mathematical Society, Providence, RI, 1992.       
11 A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Inst. Hautes Études Sci. Publ. Math., 51 (1980), 137-173.       
12 A. Katok, Hyperbolic measures and commuting maps in low dimension, Discrete Contin. Dynam. Systems, 2 (1996), 397-411.       
13 J. McCarthy, A "Tits-alternative'' for subgroups of surface mapping class groups, Trans. Amer. Math. Soc., 291 (1985), 583-612.       
14 C. P. Simon, A bound for the fixed-point index of an area-preserving map with applications to mechanics, Invent. Math., 26 (1974), 187-200.       
15 S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.       
16 S. Sternberg, Local $C^n$ transformations of the real line, Duke Math. J., 24 (1957), 97-102.       
17 J. Tits, Free subgroups in linear groups, J. Algebra, 20 (1972), 250-270.       

Go to top