2000/03/02 by Joshua A. Tempkin, Tempkin, Joshua A.
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0003007
Ph.D. Thesis, c. 75 pages with front matter, 13 postscript figures, 3 tables, LATEX using "rotating" and "subfigure" packages, master file is mythesis.tex
arxiv created 2000/03/02 · openalex publication_date 2000/03/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lyapunov exponents can be difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra "spurious" Lyapunov exponents arise that are not Lyapunov exponents of the original system. By studying the local linearization matrices that are key to the Eckmann-Ruelle method for computing Lyapunov exponents, we determine explicit formulas for the spurious exponents in certain cases. Notably, when a two-dimensional system with Lyapunov exponents A and B is reconstructed in a five-dimensional space, we show that the reconstructed system has exponents A, B, 2A, A+B, 2B.