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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6864573 |
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| author | Yanmin Niu Xiong Li |
| author_facet | Yanmin Niu Xiong Li |
| author_sort | Yanmin Niu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-04c4e43381904a2d8ea3ad449ec1b121 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-04c4e43381904a2d8ea3ad449ec1b1212025-02-03T05:52:25ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/68645736864573The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover OscillatorYanmin Niu0Xiong Li1School of Mathematical Sciences, Ocean University of China, Qingdao 266100, ChinaLaboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, ChinaIn 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.http://dx.doi.org/10.1155/2020/6864573 |
| spellingShingle | Yanmin Niu Xiong Li The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator Complexity |
| title | The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator |
| title_full | The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator |
| title_fullStr | The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator |
| title_full_unstemmed | The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator |
| title_short | The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator |
| title_sort | existence of invariant tori and quasiperiodic solutions of the nose hoover oscillator |
| url | http://dx.doi.org/10.1155/2020/6864573 |
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