In this paper, we present one of the simplest dynamical systems, inspired by Contact geometry and topology. It is a problem of double tangencies to a real curve in the plane. The solution to the problems stated in this article requires a good understanding of probability theory in the spirit of percolation theory in mathematical physics. A complete solution to the open problems presented here would be a major breakthrough in mathematics.
Received: June 9, 2019
Published online: September 24, 2019
François LalondeDépartement de mathématiques et de statistiques,
Université de Montréal, Canada.