標題: | 二維函數及其動態 The Piecewise Quadratic Map |
作者: | 王淑敏 Shu-Min Wang 莊重 Juang Jonq 應用數學系所 |
關鍵字: | 動態;二維函數;piecewise quadratic map |
公開日期: | 2002 |
摘要: | 做這篇論文的動機是藉由Udwadia與Guttalu在[9]所發表的一篇文章而引起的.我們則是考慮一個二次的函數及其動態行為.所得的結果除了涵蓋Udwadia與Guttalu在[9]所得的結果外,我們還加了更多關於渾屯特徵量的描述. Motivated by the work of Udwadia and Guttalu [9], we consider the dynamics of a piecewise quadratic map. The main results in this thesis are the following. First, we recover all the results obtained in [9]. Second, as opposed to only showing numerically that the invariant region is a chaotic attractor, we show, in this thesis, that the invariant region has a positive Lyapunov exponent. Third, more features of the chaotic properties are identified and proved. For instance, positivity of the topological entropy as well as the existence of a period three point in certain parameters' region are given. Moreover, a parameters' region, which were thought having a simple dynamics (see [9]), is shown to have the dynamics on a Cantor set being equvalient to the shift map with two symbols. |
URI: | http://140.113.39.130/cdrfb3/record/nctu/#NT910507008 http://hdl.handle.net/11536/70941 |
顯示於類別: | 畢業論文 |