A Window into the World of KAM Theory

Abstract

What happens when you periodically force a nonlinear oscillator in the absence of damping? For linear oscillators, such as the mass-on-a-spring model typically encountered in that first differential equations course, the behavior of the forced system is easily and well understood. In this article, a simple mechanical model is used to illuminate the power and beauty of the theory of Kolmogorov, Arnol’d, and Moser. Known as KAM theory, this profound 20th century mathematical achievement answers the question posed above. Model simulations illustrating the complex coexistence of regular and chaotic motions are presented. Additionally, KAM theory is placed within its historical context, namely, the quest to determine the stability of the solar system.

Publisher

Taylor and Francis

Publication Date

9-23-2020

Publication Title

Mathematics Magazine

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1080/0025570X.2020.1792238

Language

English

Format

text

Link to Full Text

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