The existence of $ \omega $-limit set for a modified Nosé-Hoover oscillator | Zendy

Qianqian Han | Zendy; Bo Deng | Zendy; XiaoSong Yang | Zendy

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The existence of $ \omega $-limit set for a modified Nosé-Hoover oscillator

Author(s) -

Qianqian Han,

Bo Deng,

XiaoSong Yang

Publication year - 2022

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2022043

Subject(s) - omega , mathematics , attractor , invariant (physics) , torus , periodic orbits , limit (mathematics) , combinatorics , physics , mathematical physics , mathematical analysis , geometry , quantum mechanics

In this paper, we prove the existence of \begin{document}$ \omega $\end{document} -limit set for a modified Nosé-Hoover oscillator. We also prove the existence of either an invariant torus or a stable periodic orbit of the oscillator. In addition, we show by numerical simulations the co-existence of both \begin{document}$ \alpha $\end{document} - and \begin{document}$ \omega $\end{document} -limit sets of various types of periodic orbits, invariant tori, and chaotic attractors.

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