Polynomial global product structure
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- by Andy Hammerlindl
- Proc. Amer. Math. Soc. 142 (2014), 4297-4303
- DOI: https://doi.org/10.1090/S0002-9939-2014-12255-6
- Published electronically: August 15, 2014
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Abstract:
An Anosov diffeomorphism is topologically conjugate to an infranilmanifold automorphism if and only if it has polynomial Global Product Structure.References
- Louis Auslander, Bieberbach’s theorems on space groups and discrete uniform subgroups of Lie groups, Ann. of Math. (2) 71 (1960), 579–590. MR 121423, DOI 10.2307/1969945
- M. I. Brin, Nonwandering points of Anosov diffeomorphisms, Dynamical systems, Vol. I—Warsaw, Astérisque, No. 49, Soc. Math. France, Paris, 1977, pp. 11–18. MR 0516499
- M. Brin, On the fundamental group of a manifold admitting a U-diffeomorphism, Soviet Math. Dokl. 19 (1978), 497–500.
- Michael Brin, Dmitri Burago, and Sergey Ivanov, Dynamical coherence of partially hyperbolic diffeomorphisms of the 3-torus, J. Mod. Dyn. 3 (2009), no. 1, 1–11. MR 2481329, DOI 10.3934/jmd.2009.3.1
- M. Brin and A. Manning, Anosov diffeomorphisms with pinched spectrum, Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980), Lecture Notes in Math., vol. 898, Springer, Berlin-New York, 1981, pp. 48–53. MR 654882
- Keith Burns and Amie Wilkinson, Dynamical coherence and center bunching, Discrete Contin. Dyn. Syst. 22 (2008), no. 1-2, 89–100. MR 2410949, DOI 10.3934/dcds.2008.22.89
- Karel Dekimpe, What an infra-nilmanifold endomorphism really should be$\ldots$, Topol. Methods Nonlinear Anal. 40 (2012), no. 1, 111–136. MR 3026104
- John Franks, Anosov diffeomorphisms, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 61–93. MR 0271990
- Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73. MR 623534
- Ku Yong Ha, Jang Hyun Jo, Seung Won Kim, and Jong Bum Lee, Classification of free actions of finite groups on the 3-torus, Topology Appl. 121 (2002), no. 3, 469–507. MR 1909004, DOI 10.1016/S0166-8641(01)00090-6
- Andrew Scott Hammerlindl, Leaf conjugacies on the torus, ProQuest LLC, Ann Arbor, MI, 2009. Thesis (Ph.D.)–University of Toronto (Canada). MR 2736718
- Andy Hammerlindl, Dynamics of quasi-isometric foliations, Nonlinearity 25 (2012), no. 6, 1585–1599. MR 2924724, DOI 10.1088/0951-7715/25/6/1585
- Andy Hammerlindl, Partial hyperbolicity on 3-dimensional nilmanifolds, Discrete Contin. Dyn. Syst. 33 (2013), no. 8, 3641–3669. MR 3021374, DOI 10.3934/dcds.2013.33.3641
- Kyung Bai Lee and Frank Raymond, Rigidity of almost crystallographic groups, Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982) Contemp. Math., vol. 44, Amer. Math. Soc., Providence, RI, 1985, pp. 73–78. MR 813102, DOI 10.1090/conm/044/813102
- Anthony Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math. 96 (1974), 422–429. MR 358865, DOI 10.2307/2373551
- Kamlesh Parwani, On 3-manifolds that support partially hyperbolic diffeomorphisms, Nonlinearity 23 (2010), no. 3, 589–606. MR 2586372, DOI 10.1088/0951-7715/23/3/009
- Michael Shub, Expanding maps, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 273–276. MR 0266251
Bibliographic Information
- Andy Hammerlindl
- Affiliation: School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
- Received by editor(s): October 1, 2012
- Received by editor(s) in revised form: January 29, 2013
- Published electronically: August 15, 2014
- Communicated by: Nimish Shah
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 4297-4303
- MSC (2010): Primary 37D20, 37D30
- DOI: https://doi.org/10.1090/S0002-9939-2014-12255-6
- MathSciNet review: 3266997