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