| Citation: |
David C. Ni. ENTROPY COMPUTATION ON THE UNIT DISC OF A MEROMORPHIC MAP[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 193-203. doi: 10.11948/2012014
|
ENTROPY COMPUTATION ON THE UNIT DISC OF A MEROMORPHIC MAP
-
Abstract
We propose a new definition of entropy based on both topological and metric entropy for the meromorphic maps. The entropy is then computed on the unit disc of a meromorphic map, which is called the extended Blaschke function, and is a nonlinear extension of the normalized Lorentz transformation.
We find that the defined entropy is computable and observe several interested results, such as maximal entropy, entropy overshoot due to topological transition, entropy reduction to zero, and scaling invariance in conjunction with parameter space.-
Keywords:
- Entropy /
- dynamical systems /
- Blaschke /
- nonlinear Lorentz transformation /
- scaling
-
-
References
[1] R. Adler, A. Konheim and M. McAndrew, Topological entropy, Trans. Amer. Math. Soc., 114(1965), 309-319. [2] W. Blaschke, Eine Erweiterung des Satzes von Vitali über Folgen analytischer Funktionen, Berichte Math.-Phys. Kl., Sächs. Gesell. der Wiss. Leipzig, 67(1915), 194-200. [3] Conference proceedings of Frontiers of Complex dynamics (in preparation), Banff Center, Alberta, Canada, Feb. 2011. [4] T. Donarowicz, Entropy in Dynamical Systems, Cambridge University Press, May 2011(ISBN:9780521888851). [5] J. Milnor, Is Entropy Effectively Computable, Jan. 2002. [6] D. C. Ni, Numerical Studies of Lorentz Transformation, presented in 7th EASIAM, Kitakyushu, Japan, June, 2011, 27-29. -
-
Export File
Citation
David C. Ni. ENTROPY COMPUTATION ON THE UNIT DISC OF A MEROMORPHIC MAP[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 193-203. doi: 10.11948/2012014
DownLoad: