RT Report T1 Smoothness, degrees of freedom and Liapunov exponents of a time series A1 Mera Rivas, María Eugenia A1 Morán Cabré, Manuel AB We propose a set of tests addressing the issue of determining whether the generating law of a time series is a stochastic process or a chaotic dynamics. In the latter case, we test the smoothness and find the number of degrees of freedom of the underlying dynamics. We propose an adaptation of Eckmann and Ruelle algorithm for the computation of the Liapunov exponents of a time series. This algorithm computes efficiently the whole Liapunov spectrum of the observed dynamics, avoiding the problem of the spurious exponents. PB Facultad de Ciencias Económicas y Empresariales. Decanato SN 2255-5471 YR 2000 FD 2000 LK https://hdl.handle.net/20.500.14352/64136 UL https://hdl.handle.net/20.500.14352/64136 LA eng NO Broomhead, D.S. and G.P. King. Extracting Qualitative Dynamics from Experimental Data, Physica 20D, (1986), 217-236.Broomhead, D.S. and G.P. King. Phase Portraits from a Time Series: A Singular System Approach, Nuclear Physics B, 2, (1987), 379-390.Brown, R., P. Bryan and H. Abarbanel. Computing the Liapunov spectnun of a dynarnical systern from an observed tierne series. Physical Review A, 43, (1991), 2787-2806.Cawley, R. and Guan-Hsong Hsu. Local Geometric Projection Method for Noise Reduction in Chaotic Maps and Flows, Physical Review A, 46, 6, (1992), 3057-3082.Eckrnann, J.P. and D. Ruelle. Ergodic Theory of Chaos and Strange Attractors, Reviews of Modern Physics, 57, 3, (1985), 617-656.Eckmann, J.P., S.O. Kamphorst, D. Ruelle and S. Ciliberto. Liapunov Exponents from Time Series, Physical Review A, 34, 6, (1986), 4971-4979.Gill, P.E., W. Murray and M.H. Wright. Numerical Linear Algebra and Optimization. Volume 1. Addison-Wesley Publishing Cornpany (1991).Grassberger, P. An Optimized Box-Assisted Algorithm for Fractal Dimcnsions, Phys. Lett. A, 148, (1990), 63-68.Kshirsagar, A.M. Multivariate Analysis. Marcel Dekker. NY (1972).Mattila, P. Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability. Cambridge University Press (1995).Mera, M.E. and M. Morán. Convergence of the Eckmann and Ruelle Algorithm for the Estimation of Liapunov Exponents, (forthcoming in Ergodie Theory and Dynamical Systems).Mera, M.E. and M. Morán. Lp(µ)-Estimation of Tangent Maps, Journal of Mathematical Analysis and Applications 235, (1999), 454-469.Sano, M. and Y. Sawada. Measurement of the Lyapunov Spectrurn from a Chaotic Time Series. Physycal Review Letters, 55, 10, (1985), 1082-1085.Sauer, T., York, J.A. and Casdagli, M. Embedology. Journal of Statistical Physics, 65, 3/4, (1992), 579-616.Takens, F. Detecting Strange Attractors in Turbulence, Dynamical Systems and Turbulence. Lectures Notes in Mathematics, 898, 396, (1981). DS Docta Complutense RD 28 abr 2024