The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator
Joint Authors
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-11
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
In this paper, we consider an equivalent form of the Nosé–Hoover oscillator, x′=y,y′=−x−yz, and z′=y2−a, where a is a positive real parameter.
Under a series of transformations, it is transformed into a 2-dimensional reversible system about action-angle variables.
By applying a version of twist theorem established by Liu and Song in 2004 for reversible mappings, we find infinitely many invariant tori whenever a is sufficiently small, which eventually turns out that the solutions starting on the invariant tori are quasiperiodic.
The discussion about quasiperiodic solutions of such 3-dimensional system is relatively new.
American Psychological Association (APA)
Niu, Yanmin& Li, Xiong. 2020. The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator. Complexity،Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1143419
Modern Language Association (MLA)
Niu, Yanmin& Li, Xiong. The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator. Complexity No. 2020 (2020), pp.1-9.
https://search.emarefa.net/detail/BIM-1143419
American Medical Association (AMA)
Niu, Yanmin& Li, Xiong. The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator. Complexity. 2020. Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1143419
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1143419