Rigorous numerical Estimation of Lyapunov exponents and Invariant Measures of Iterated Function Systems and Random Matrix Products

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[1]  J. Elton An ergodic theorem for iterated maps , 1987, Ergodic Theory and Dynamical Systems.

[2]  Michael Dellnitz,et al.  An adaptive subdivision technique for the approximation of attractors and invariant measures , 1998 .

[3]  Miguel A. Rodriguez,et al.  A MULTIFRACTAL ANALYSIS OF IFSP INVARIANT MEASURES WITH APPLICATION TO FRACTAL IMAGE GENERATION , 1996 .

[4]  Michael C. Mackey,et al.  Chaos, Fractals, and Noise , 1994 .

[5]  Abraham Boyarsky,et al.  A MATRIX METHOD FOR APPROXIMATING FRACTAL MEASURES , 1992 .

[6]  K. Falconer Techniques in fractal geometry , 1997 .

[7]  S. Ulam Problems in modern mathematics , 1964 .

[8]  A. Crisanti,et al.  Products of random matrices in statistical physics , 1993 .

[9]  Petri,et al.  Generalized Lyapunov exponents for products of correlated random matrices. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Mees,et al.  Estimation of Lyapunov exponents of dynamical systems using a spatial average. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  M. Barnsley,et al.  A new class of markov processes for image encoding , 1988, Advances in Applied Probability.

[12]  Mario Peruggia Discrete Iterated Function Systems , 1993 .

[13]  H. Furstenberg,et al.  Random matrix products and measures on projective spaces , 1983 .

[14]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory , 1980 .

[15]  Jaroslav Stark Iterated Function Systems as neural networks , 1991, Neural Networks.

[16]  M. Mackey,et al.  Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics , 1998 .