Jan Philipp Dietrich:
Attractor reconstruction in the Fourier space

April 23, 2008, 2:30pm
Building 19, Room 4.15 University Potsdam, Campus Neues Palais

There are several methods for attractor reconstruction. The first and mostly 
used one is the time-delay method invented bei Takens [1][2]. 
But also other methods as e.g. derivation [3] or integration [4] 
offer advantages for some applications. All of them lead to a proper embedding of the original system.
So the question is: Why do all these methods produce similar results? 
Is there any general structure which is unifying all of them to only one 
general reconstruction method? Is there a chance to combine them to get 
reconstructions with customized properties? 
Possibly a answer can be found by comparing all these methods in frequency space.

[1] F.Takens (1981). "Detecting strange attractors in turbulence". 
D.A. Rand and L.-S. Young Dynamical Systems and Turbulence, 
Lecture Notes in Mathematics, vol. 898: 366-381, Springer-Verlag.

[2] Tim Sauer, James A.Yorke, and Martin Casdagli (1991). 
"Embedolgy". Journal of Statistical Physics 65: 579-616

[3] N.Packard, J. Crutchfield, D. Farmer and R.Shaw (1980). 
"Geometry from time series". Physical Review Letters 45: 712-716.

[4] R.Gilmore (1998). "Topological analysis of chaotic dynamical systems". 
Reviews of Modern Physics 70: 1455-1529