Discussion on the Geometric Structure of Strange Attractor
LIU Zengrong, CAO Yongluo
Laboratory for Nonlinear Mechanics of Continuous Media,
Institute of Mechanics, Academia of Sinica
And Department of Mathematics, Suzhou University, Suzhou 215006
Discussion on the Geometric Structure of Strange Attractor
LIU Zengrong;CAO Yongluo
Laboratory for Nonlinear Mechanics of Continuous Media,
Institute of Mechanics, Academia of Sinica
And Department of Mathematics, Suzhou University, Suzhou 215006
Abstract： We discuss the transversal heteroclinic cycle formed by hyperbolic periodic points of diffeomorphism on the differential manifold. We point out that every possible kind of transversal heteroclinic cycle has the Smalehorse property and the unstable manifolds of hyperbolic periodic points have the closure relation mutually. Therefore the strange attractor may be the closure of unstable manifolds of a countable number of hyperbolic periodic points. The Hénon mapping is used as an example to show that the conclusion is reasonable.
LIU Zengrong;CAO Yongluo. Discussion on the Geometric Structure of Strange Attractor[J]. 中国物理快报, 1991, 8(10): 503-506.
LIU Zengrong, CAO Yongluo. Discussion on the Geometric Structure of Strange Attractor. Chin. Phys. Lett., 1991, 8(10): 503-506.
1991, Vol. 8 
