QUALITATIVE ANALYSIS OF A GENERALIZED NOSacuteE-HOOVER OSCILLATOR

In this paper, we analyze the qualitative dynamics of a generalized Nose '-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) is an element of R3|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 R3.