|
Quasi-periodic Orbits in Siegel Disks/Balls and the Babylonian Problem
Yoshitaka Saikiabc, James A. Yorkec a Graduate School of Business Administration, Hitotsubashi University
2-1 Naka, Kunitachi, Tokyo 186-8601, Japan
b JST PRESTOб 4-1-8 Honcho, Kawaguchi-shi, Saitama 332-0012, Japan
c University of Maryland, College Park, MD 20742, USA
Аннотация:
We investigate numerically complex dynamical systems where a fixed point is surrounded by a disk or ball of quasi-periodic orbits, where there is a change of variables (or conjugacy) that converts the system into a linear map. We compute this “linearization” (or conjugacy) from knowledge of a single quasi-periodic trajectory. In our computations of rotation rates of the almost periodic orbits and Fourier coefficients of the conjugacy, we only use knowledge of a trajectory, and we do not assume knowledge of the explicit form of a dynamical system. This problem is called the Babylonian problem: determining the characteristics of a quasi-periodic set from a trajectory. Our computation of rotation rates and Fourier coefficients depends on the very high speed of our computational method “the weighted Birkhoff average”.
Ключевые слова:
quasi-periodic orbits, rotation rates, weighted Birkhoff averaging, Siegel disk, Siegel ball.
Поступила в редакцию: 24.09.2018 Принята в печать: 30.10.2018
Образец цитирования:
Yoshitaka Saiki, James A. Yorke, “Quasi-periodic Orbits in Siegel Disks/Balls and the Babylonian Problem”, Regul. Chaotic Dyn., 23:6 (2018), 735–750
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd363 https://www.mathnet.ru/rus/rcd/v23/i6/p735
|
Статистика просмотров: |
Страница аннотации: | 134 | Список литературы: | 26 |
|