The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator. (11th November 2020)

• Record Type: Journal Article
• Authors: Niu, Yanmin; Li, Xiong
• Other Names: Floquet Thierry Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-11-11
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/6864573
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : In this paper, we consider an equivalent form of the Nosé–Hoover oscillator, x ′ = y, y ′ = − x − y z, and z ′ = y 2 − 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.