田光復臺灣大學：數學研究所何志偉Ho, Chih-WeiChih-WeiHo2007-11-282018-06-282007-11-282018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/59469When studying a physical phenomenon experimentally following the evolution of time, we measured and collected relevant one dimensional data and considered it correct even when the data appeared chaotic, we assumed the phenomenon is controlled by a strange attractor in an unknown phase space. This point of view induces the delay reconstruction method and embedding theorems due to Whitney, Takems, Sauer, Yorke, Casdagli. What follows then is to estimate the dimension of that strange attractor by Grassberger and Procaccia (D2 dimension) method in that embedded space with the dimension, or higher. Before doing so I tried the idea of making a description of the classical Cantor set which is defined only through logic and is an uncountable set while any time series is at most countable. Then I tried the same method to any relaxed Cantor set and “calculate” the dimension and demonstrate that time series description is applicable. Furthermore, from two sets of experimental data (1. Nuclear Magnetic Resonance (NMR) 2.Arrhythmias), they and we use the same algorithm to estimate the “fractal” dimension of the attractor of the dynamical system.Contents Chapter 1 Introduction, from classical to chaotic phenomenon 1 Chapter 2 Time series describing original and relaxed Cantor set 5 2.1 Method of delay reconstruction of time series and the embedding theorem of a presumably deterministic system 5 2.2 Grassberger and Procaccia algorithmic estimation of correlation dimension of a phase curve of time series assumed in a phase space converging to a strange attractor 6 2.3 A time series describing the geometric Cantor set, estimating its correlation dimension in stead of the geometric box counting dimension 7 2.4 Time series method effectively estimating correlation dimension of the relaxed Cantor set 10 Chapter 3 Reconstruction and estimation of fractal dimension of Nuclear Magnetic Resonance (NMR) laser data and arrhythmia data of human atrium 13 3.1 NMR and analysis of data of Kantz and Schreiber 13 3.2 Arrhythmia data of base line compare to application of propafanone (ppf) of human heart15 Chapter 4 Discussions of the Situation 18 References 19506176 bytesapplication/pdfen-US時間序列相空間與相空間曲線奇異吸引子延遲重構嵌入空間classical and relaxed Cantor setBelousov-Zhabotinskii reaction核磁共振心律不整Grassberger and Procaccia (D2 dimension)time seriesphase space and curvestrange attractordelay reconstructionembedding spaceNMRArrhythmiathesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59469/1/ntu-95-R92221021-1.pdf