Ergodic properties of folding maps on spheres

Almut Burchard; Gregory R. Chambers; Anne Dranovski

doi:10.3934/dcds.2017049

Article Contents

2017, Volume 37, Issue 3: 1183-1200. Doi: 10.3934/dcds.2017049

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Ergodic properties of folding maps on spheres

1.
University of Toronto, Department of Mathematics, 40 St. George St., Room 6290, Toronto, ON M5S 2E4, Canada
2.
University of Chicago, Department of Mathematics, 5734 S. University Avenue, Room 208C, Chicago, IL 60637, USA

* Corresponding author: A. Burchard
* Corresponding author: A. Burchard

Received: May 2016

Revised: November 2016

Published: May 2017

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Abstract

We consider the trajectories of points on $ \mathbb{S}^{d-1} $ under sequences of certain folding maps associated with reflections. The main result characterizes collections of folding maps that produce dense trajectories. The minimal number of maps in such a collection is d+1.

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Mathematics Subject Classification: 20F55, 37A45, 51F15, 60J15.

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