The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator

Joint Authors

Niu, Yanmin
Li, Xiong

Source

Complexity

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

Philosophy

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