Computer-Assisted Methods for Studying Periodic Orbits on R4

Abstract

Abstract. We apply numeric and rigorous interval computer-assisted methods to studying periodic orbits of dynamical systems on R4, with particular attention given to the family of systems that are the ana- log in R4 to triangular billiards, originally discovered by Ferran Valdez. We present our libraries implementing numerical experiments for ex- ploring dynamical systems on C2 and develop implementations, along with an experimentation framework. Implemented tools include nonrigor- ous numerical simulations for Newton’s method and generating Poincaré maps, key elements of C0 and C1 Lohner-type algorithms, and multiple- dimension interval calculus tools.