1981-Takens嵌入定理经典文献.pdfVIP

Detecting strange a t t r a c t o r s in t u r b u l e n c e . Floris Takens. 1. Introduction. Since [19] was written, much m o r e accurate experiments on the onset of turbulence have been made, especially by F e n s t e r m a c h e r , Swinney, Gollub and Benson [6,8,9,10]. These new experimental data should be interpreted according to [19] in t e r m s of strange attractors, or they should falsify the whole picture given in that paper. F o r such interpretations one uses in general the so-called power spectrum. It is however not at all clear how to reconstruct tt~e strange a t t r a c t o r s from a power s p e c t r u m (with continuous parts); even w o r s e : how can one see whether a given power spectrum (with continuous parts) might have been generated by a strange a t t r a c t o r ? In this paper I present _proc_e_dure___s _t_o_deci_de_ whether one may attribute certain} ..experimen_t.aj datta___as_ in the onset o f turbulences_ to the p r e s e n c e of strange a t t r a c t o r s . These procedures consist of algorithms, to be applied to the experimental data itself and not to the power spectrum; in fact, I doubt whether the power spectrum contains the relevant information. In o r d e r to describe the problems and results, treated in this paper, in m o r e detail, I shall first review the ideas of [19], also comparing them witl~ those e~posed by Landau and Lifschitz [13], in relation with the flow between two rotating cylinders. It wa