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arXiv · 0709.4646

Positve Entropy Geodesic Flows on Nilmanifolds

Leo T. Butler·Vassili Gelfreich
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Abstract

Let T be the nilpotent group of 4 x 4 real upper triangular matrices. In this note we show that the Euler equations of certain left-invariant riemannian metrics on T have a horseshoe. We also show, with the aid of a numerical computation of a Melnikov-type integral, that the Euler equations of the sub-riemannian Carnot metric on T has a horseshoe. This sharpens an earlier result of Montgomery, Shapiro and Stolin who had shown that the equations are algebraically non-integrable.

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Leo T. Butler, Vassili Gelfreich. 2007-09-28. Positve Entropy Geodesic Flows on Nilmanifolds. https://doi.org/10.1088/0951-7715%2F21%2F7%2F002

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