Ergodic properties of folding maps on spheres

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 $d+1$.

18 pages; Accepted for publication in Discrete and Continuous Dynamical Systems - Series A

References in corpus (2)

• Rate of convergence of random polarizations
• Approximation of symmetrizations by Markov processes

Cited by in corpus (2)

• Convergence of symmetrization processes
• Full rotational symmetry from reflections or rotational symmetries in finitely many subspaces