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### Positive-entropy geodesic flows on nilmanifolds

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Butler, Leo T. and Gelfreich, Vassili.
(2008)
*Positive-entropy geodesic flows on nilmanifolds.*
Nonlinearity, Volume 21
(Number 7).
pp. 1423-1434.
ISSN 0951-7715

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1088/0951-7715/21/7/002

## Abstract

Let T-n be the nilpotent group of real n x n upper-triangular matrices with 1s on the diagonal. The Hamiltonian flow of a left-invariant Hamiltonian on T*T-n naturally reduces to the Euler flow on t(n)*, the dual of t(n) = Lie(T-n). This paper shows that the Euler flows of the standard Riemannian and sub-Riemannian structures of T-4 have transverse homoclinic points on all regular coadjoint orbits. As a corollary, left-invariant Riemannian metrics with positive topological entropy are constructed on all quotients D\T-n where D is a discrete subgroup of T-n and n >= 4.

Item Type: | Journal Article |
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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: | 0951-7715 |

Official Date: | July 2008 |

Volume: | Volume 21 |

Number: | Number 7 |

Number of Pages: | 12 |

Page Range: | pp. 1423-1434 |

Identification Number: | 10.1088/0951-7715/21/7/002 |

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 two-step nilmanifolds Ergod. |

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

Data sourced from Thomson Reuters' Web of Knowledge

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