The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator
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 theo...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6864573 |
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| Summary: | 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. |
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| ISSN: | 1076-2787 1099-0526 |