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Positiveentropy geodesic flows on nilmanifolds
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Butler, Leo T. and Gelfreich, Vassili. (2008) Positiveentropy geodesic flows on nilmanifolds. Nonlinearity, Volume 21 (Number 7). pp. 14231434. ISSN 09517715
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Official URL: http://dx.doi.org/10.1088/09517715/21/7/002
Abstract
Let Tn be the nilpotent group of real n x n uppertriangular matrices with 1s on the diagonal. The Hamiltonian flow of a leftinvariant Hamiltonian on T*Tn naturally reduces to the Euler flow on t(n)*, the dual of t(n) = Lie(Tn). This paper shows that the Euler flows of the standard Riemannian and subRiemannian structures of T4 have transverse homoclinic points on all regular coadjoint orbits. As a corollary, leftinvariant Riemannian metrics with positive topological entropy are constructed on all quotients D\Tn where D is a discrete subgroup of Tn and n >= 4.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics Q Science > QC Physics 

Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Entropy, Differentiable manifolds, Geodesic flows  
Journal or Publication Title:  Nonlinearity  
Publisher:  Institute of Physics Publishing Ltd.  
ISSN:  09517715  
Official Date:  July 2008  
Dates: 


Volume:  Volume 21  
Number:  Number 7  
Number of Pages:  12  
Page Range:  pp. 14231434  
Identifier:  10.1088/09517715/21/7/002  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
References:  [1] Butler L T 2003 Integrable geodesic ﬂows with wild ﬁrst integrals: the case of twostep nilmanifolds Ergod. 

URI:  http://wrap.warwick.ac.uk/id/eprint/29743 
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