Partial hyperbolicity on 3-dimensional nilmanifolds

Andy Hammerlindl

doi:10.3934/dcds.2013.33.3641

Article Contents

2013, Volume 33, Issue 8: 3641-3669. Doi: 10.3934/dcds.2013.33.3641

This issue Previous Article Porous media equations with two weights: Smoothing and decay properties of energy solutions via Poincaré inequalities Next Article Branch interactions and long-term dynamics for the diblock copolymer model in one dimension

Partial hyperbolicity on 3-dimensional nilmanifolds

Andy Hammerlindl^1,

1.
School of Mathematics and Statistics, University of Sydney, NSW, 2006

Received: July 31, 2012

Revised: October 31, 2012

Published: July 2013

Abstract Related Papers Cited by

Abstract

Every partially hyperbolic diffeomorphism on a 3-dimensional nilmanifold is leaf conjugate to a nilmanifold automorphism. Moreover, if the nilmanifold is not the 3-torus, the center foliation is an invariant circle bundle.

Keywords:

Partial hyperbolicity,
classification.

Mathematics Subject Classification: Primary: 37D30.

Citation:

Related Papers

Cited by

References

[1]	L. Auslander, Bieberbach's theorems on space groups and discrete uniform subgroups of Lie groups, Annals of Math., 71 (1960), 579-590.
[2]	M. Brin, On dynamical coherence, Ergod. Th. and Dynam. Sys., 23 (2003), 395-401.doi: 10.1017/S0143385702001499.
[3]	M. Brin, D. Burago and S. Ivanov, Dynamical coherence of partially hyperbolic diffeomorphisms of the 3-torus, Journal of Modern Dynamics, 3 (2009), 1-11.doi: 10.3934/jmd.2009.3.1.
[4]	J. Franks, Anosov diffeomorphisms on tori, Transactions of the American Mathematical Society, 145 (1969), 117-124.
[5]	J. Franks, Anosov diffeomorphisms, Global Analysis: Proceedings of the Symposia in Pure Mathematics, 14 (1970), 61-93.
[6]	A. Hammerlindl, "Leaf Conjugacies on the Torus," Ph.D thesis, University of Toronto, 2009.
[7]	F. Rodriguez Hertz, M. A. Rodriguez Hertz and R. Ures, Partial hyperbolicity and ergodicity in dimension three, Journal of Modern Dynamics, 2 (2008), 187-208.doi: 10.3934/jmd.2008.2.187.
[8]	M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds," 583 of Lecture Notes in Mathematics, Springer-Verlag, 1977.
[9]	A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429.
[10]	K. Parwani, On 3-manifolds that support partially hyperbolic diffeomorphisms, Nonlinearity, 23 (2010), 589-606.doi: 10.1088/0951-7715/23/3/009.