Local and Global Lyapunov exponents |
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| Authors: | A. Eden C. Foias R. Temam |
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| Affiliation: | (1) Department of Mathematics, Swain East No. 222, Indiana University, 47405 Bloomington, Indiana;(2) Department of Mathematics, Arizona State University, 85287-1804 Tempe, Arizona;(3) Department of Mathematics, Swain East No. 310, and The Institute for Applied Mathematics & Scientific Computing, Indiana University, 618 East 3rd Street, 47405 Bloomington, Indiana;(4) Laboratoire d'Analyse Numérique, Bat. 425, Université Paris-Sud, 91405 Orsay, France;(5) Department of Mathematics, Swain East No. 317, The Institute for Applied Mathematics & Scientific Computing, Indiana University, 47405 Bloomington, Indiana |
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| Abstract: | Various properties of Local and Global Lyapunov exponents are related by redefining them as the spectral radii of some positive operators on a space of continuous functions and utilizing the theory developed by Choquet and Foias. These results are then applied to the problem of estimating the Hausdorff dimension of the global attractor and the existence of a critical trajectory, along which the Lyapunov dimension is majorized, is established. Using this new estimate, the existing dimension estimate for the global attractor of the Lorenz system is improved. Along the way a simple relation between topological entropy and the fractal dimension is obtained. |
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| Keywords: | Attractors Lyapunov exponents Lyapunov dimension Lorenz equations entropy |
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