On Some Dynamical Properties of Interval Maps

• Main Authors: Kong-Li Liu, 劉孔驪
• Other Authors: Jonq Juang
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/32437092978418995733

碩士 === 國立交通大學 === 應用數學系 === 90 === On Some Dynamical Properties of Interval Maps Student: Kong-Li Liu Adviser: Jonq Juang Department of Applied Mathematics National Chiao Tung University Hsinchu 30050, Taiwan, R.O.C. Abstract The dissertation contains three chapters. The topic of chapter 1 is to discuss the set {x belongs to I:S(x)=K(f)} for a unimodal map. First, we consider all possible scenarios. The main techniques to achieve so are those introduced in the proof of Theorem 1.2.10. Let fr(x)=rx(1-x) be the quadratic map. We then use renormalization techniques to derive the precise form of the set {x belongs to I:S(x)=K(fr)} as the family of fr undergoes period doubling bifurcation. In chapter 2, we devote our attention to checking whether some conclusions concerning the assumption " Sf<0 on I " in §1.11, §1.19([1]) still hold if we substitute it for "sensitivity on initial data on I." In the third chapter, we will first provide the generalization of definitions in §1.18([1]) and use the notations developed by J. Milnor and W. Thurston([4]) throughout this chapter. Moreover, we derive a sufficient condition to guarantee the admissibility of symbolic sequences associated with piecewise-monotone maps(i.e. l-modal maps, l>1 ). Additionally, some assertions about the set of periodic points of such maps will be included.