Eur. Phys. J. B (2015) 88: 78
https://doi.org/10.1140/epjb/e2015-60062-1

Regular Article

The invariant tori of knot type and the interlinked invariant tori in the Nosé-Hoover oscillator

¹ School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P.R. China
² Department of Mathematics and Physics, Hefei University, Hefei 230601, P.R. China

^a e-mail: xsyang@hust.edu.cn

Received: 21 January 2015
Received in final form: 17 February 2015
Published online: 25 March 2015

Abstract

We revisit the Nosé-Hoover oscillator in this paper and show the existence of some averagely conservative regions which are filled with an infinite sequence of nested tori. Depending on initial conditions, some invariant tori are of trefoil knot type, while the others are of trivial knot type. Moreover, we present a variety of interlinked invariant tori whose initial conditions are chosen from different averagely conservative regions and give all the interlinking numbers of those interlinked tori, showing that the oscillator possesses so rich dynamic properties.