volume 26, issue 10, P5337 2021
DOI: 10.3934/dcdsb.2020346
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Qianqian Han, Xiao-Song Yang

Abstract: In this paper, we analyze the qualitative dynamics of a generalized Nosé-Hoover oscillator with two parameters varying in certain scope. We show that if a solution of this oscillator will not tend to the invariant manifold {(x, y, z) ∈ R 3 |x = 0, y = 0}, it must pass through the plane z = 0 infinite times. Especially, every invariant set of this oscillator must have intersection with the plane z = 0. In addition, we show that if a solution is quasiperiodic, it must pass through at least five quadrants of R 3 .

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