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

Yanmin Niu and Xiong Li

Complexity, 2020, vol. 2020, 1-9

Abstract:

In this paper, we consider an equivalent form of the Nosé–Hoover oscillator, , where 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 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:6864573

DOI: 10.1155/2020/6864573

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