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Classification of expansive attractors on surfaces

Published online by Cambridge University Press:  23 November 2010

MARCY BARGE and
BRIAN F. MARTENSEN
MARCY BARGE
Affiliation:
Department of Mathematics, Montana State University, Bozeman, MT 59717, USA (email: barge@math.montana.edu)
BRIAN F. MARTENSEN
Affiliation:
Department of Mathematics and Statistics, Minnesota State University, Wissink 273, Mankato, MN 56001, USA (email: martensen@mnsu.edu)
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Abstract

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We prove the conjecture of F. Rodriguez Hertz and J. Rodriguez Hertz [Expansive attractors on surfaces. Ergod. Th. & Dynam. Sys.26(1) (2006), 291–302; MR 2201950(2006j:37049)] that every non-trivial transitive expansive attractor of a homeomorphism of a compact surface is a derived from pseudo-Anosov attractor.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 6 , December 2011, pp. 1619 - 1639
Copyright
Copyright © Cambridge University Press 2010

References

[Bro60]Brown, M.. Some applications of an approximation theorem for inverse limits. Proc. Amer. Math. Soc. 11 (1960), 478–483; MR 0115157(22#5959).CrossRefGoogle Scholar
[BS07]Barge, M. and Swanson, R.. Rigidity in one-dimensional tiling spaces. Topology Appl. 154(17) (2007), 3095–3099; MR 2355514(2008k:37039).CrossRefGoogle Scholar
[Hir90]Hiraide, K.. Expansive homeomorphisms of compact surfaces are pseudo-Anosov. Osaka J. Math. 27(1) (1990), 117–162; MR 1049828(91b:58184).Google Scholar
[HM08]Holton, C. and Martensen, B. F.. Embedding tiling spaces in surfaces. Fund. Math. 201(2) (2008), 99–113; MR 2448414.CrossRefGoogle Scholar
[Lew89]Lewowicz, J.. Expansive homeomorphisms of surfaces. Bol. Soc. Brasil. Mat., Nova Sér. 20(1) (1989), 113–133; MR 1129082(92i:58139).CrossRefGoogle Scholar
[Mat82]Mather, J. N.. Topological proofs of some purely topological consequences of Carathéodory’s theory of prime ends. Selected Studies: Physics-Acstrophysics, Mathematics, History of Science. North-Holland, Amsterdam, 1982, pp. 225–255; MR 662863(84k:57004).Google Scholar
[Moo25]Moore, R. L.. Concerning upper semi-continuous collections of continua. Trans. Amer. Math. Soc. 27(4) (1925), 416–428.CrossRefGoogle Scholar
[Mos86]Mosher, L.. The classification of pseudo-Anosovs. Low-dimensional Topology and Kleinian Groups (Coventry/Durham, 1984) (London Mathematical Society Lecture Note Series, 112). Cambridge University Press, Cambridge, 1986, pp. 13–75; MR 903858(89f:57016).Google Scholar
[RHRH06]Rodriguez Hertz, F. and Rodriguez Hertz, J.. Expansive attractors on surfaces. Ergod. Th. & Dynam. Sys. 26(1) (2006), 291–302; MR 2201950(2006j:37049).CrossRefGoogle Scholar
[Sma67]Smale, S.. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747–817; MR 0228014(37#3598).CrossRefGoogle Scholar
[TW98]Tymchatyn, E. D. and Walker, R. B.. Taming the Cantor fence. Topology Appl. 83(1) (1998), 45–52; MR 1601638(99f:54055).CrossRefGoogle Scholar
[Wil70]Williams, R. F.. Classification of one dimensional attractors. Global Analysis (Proceedings of Symposia in Pure Mathematics, XIV, Berkeley, CA, 1968). American Mathematical Society, Providence, RI, 1970, pp. 341–361; MR 0266227(42#1134).CrossRefGoogle Scholar