研究區間算法如何解決勞倫茲吸子存在性之問題

Study of interval arithmetic The problem of existence of Lorenz attractor

黃千豪(Chain-Hau Huang)

指導教授 ： 田光復

國立臺灣大學/理學院/數學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.01948

摘要

無資料

關鍵字

Lorenz ； 吸子 ； 區間算法

並列摘要

The 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.

並列關鍵字

Lorenz ； attractor ； interval arithmetic

參考文獻

[1] J. Guckenheimer, A strange, strange attractor, in: The Hopf Bifurcation and its Applications (J. E. Marsden and M. McCracken, eds.), Springer-Verlag, New York, 1976.

[2] J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer-Verlag, New York, 1983.

[4] E. N. Lorenz, Deterministic non-periodic flow, J. Atmospheric Sci. 20 (1963), 130–141.

[5] R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1966.

[7] J. Murdock, Normal forms and unfoldings for local dynamical systems, Springer-Verlag, New York, 2003.