A computer-assisted proof of symbolic dynamics in Hyperion's rotation

被引：6

作者：

Gierzkiewicz, Anna ^{[1
]}

Zgliczynski, Piotr ^{[2
]}

机构：

[1] Agr Univ Krakow, Dept Appl Math, Ul Balicka 253c, PL-30198 Krakow, Poland

[2] Jagiellonian Univ, Inst Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 2019年 / 131卷 / 07期

关键词：

Computer-assisted proof; Hyperion; Symbolic dynamics; Interval Newton method;

D O I：

10.1007/s10569-019-9910-8

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

Hyperion is a moon of Saturn, known of its non-round shape. Its rotation is often modelled by equations of motion of an ellipsoidal satellite. The model is expected to be chaotic for a large range of parameters. The paper contains a rigorous proof of the existence of symbolic dynamics in the model. In other words, there exist infinitely many periodic orbits of arbitrary periods coded by the sequences of two symbols. The proofs are computer assisted, based on the interval arithmetic by the use of CAPD C++ library.

引用

页数：17

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