Open AccessThe existence of $ \omega $-limit set for a modified Nosé-Hoover oscillator
Author(s) -
Qian-Qian Han,
Bo Deng,
XiaoSong Yang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022043
Subject(s) - omega , mathematics , attractor , invariant (physics) , torus , periodic orbits , limit (mathematics) , combinatorics , physics , mathematical physics , mathematical analysis , geometry , quantum mechanics
In this paper, we prove the existence of \begin{document}$ \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.