田光復Tien, Kuang-Fu臺灣大學:數學研究所黃千豪Huang, Chain-HauChain-HauHuang2010-05-052018-06-282010-05-052018-06-282009U0001-1901200900394200http://ntur.lib.ntu.edu.tw//handle/246246/180605The basis of this thesis is to study intensively what is Tucker’s idea, mathematical theoretical basis, rigorous computation in his article and prove to myself what is not very clearly proved, and hopefully apply this new method to establish answers to the existence of attractors of other system.Contentshapter 1. Basics of Lorenz equation 1.1 What is Lorenz equation and their properties 1.2 Dynamics of Lorenz equation 6.3 Does Lorenz attractor exist? 9hapter 2. Interval arithmetic and its application 11.1 Linear change of variables of the Lorenz equations 11.2 Good Pick for return plane 13.3 Directed rounding 13.4 Interval arithmetic 14.5 Local Euler Poincare ́ box and local Euler Poincare ́ map 17.6 Search for global Poincare ́ map 24.7 Bisection process 28hapter 3. A typical one-dimensional chaotic map 30.1 One-dimensional map with topological transitivity 30.2 Estimation for evolution of cone 31.3 Estimation for evolution of Expansion 33.4 Existence for forward invariant cone field 36.5 Information for expansions of tangent vectors in cone 38hapter 4. Dynamics near the origin 40.1 Local change of coordinates 40.2 Estimation of normal form flow 42eferences 47application/pdf1131643 bytesapplication/pdfen-USLorenz吸子區間算法attractorinterval arithmeticthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/180605/1/ntu-98-R94221029-1.pdf