KNOTTED PERIODIC ORBITS AND CHAOTIC BEHAVIOR OF A CLASS OF THREE-DIMENSIONAL FLOWS
2011 ◽
Vol 21
(09)
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pp. 2505-2523
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This paper considers a class of three-dimensional systems constructed by rotating some planar symmetric polynomial vector fields. It shows that this class of systems has infinitely many distinct types of knotted periodic orbits, which lie on a family of invariant torus. For two three-dimensional systems, exact explicit parametric representations of the knotted periodic orbits are given. For their perturbed systems, the chaotic behavior is discussed by using two different methods.
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2007 ◽
Vol 17
(09)
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pp. 3295-3302
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2006 ◽
Vol 16
(02)
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pp. 369-381
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2005 ◽
Vol 25
(3)
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pp. 621-627
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2004 ◽
Vol 198
(2)
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pp. 374-380
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Keyword(s):
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