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Title: Computer-Assisted Methods for Studying Periodic Orbits on R4
Authors: Wang, Yuan
Advisors: Gomez-Serrano, Javier
Contributors: Vicol, Vlad C.
Department: Mathematics
Certificate Program: Applications of Computing Program
Class Year: 2017
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.
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Mathematics, 1934-2020

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