# American Institute of Mathematical Sciences

March  2017, 37(3): 1183-1200. doi: 10.3934/dcds.2017049

## 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

Received  May 2016 Revised  November 2016 Published  December 2016

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.

Citation: Almut Burchard, Gregory R. Chambers, Anne Dranovski. Ergodic properties of folding maps on spheres. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1183-1200. doi: 10.3934/dcds.2017049
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