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The invariant tori of knot type and the interlinked invariant tori in the Nos\'e-Hoover system
We revisit the famous Nos\'e-Hoover system 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 this
quadratic system possesses so rich dynamic properties.Comment: 8 pages,8 figure
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