On computing the entropy of the Henon attractor |
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Authors: | James H Curry |
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Institution: | (1) Institut des Hautes Etudes Scientifiques, 35, route de Chartres, 91440 Bures-sur-Yvette, France;(2) Present address: Mathematics Department, University of Colorado, Box 426, 80309 Boulder, Colorado, USA |
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Abstract: | In a recent article D. Ruelle inLecture Notes in Physics, No. 80 (Springer, Berlin, 1978)] has conjectured that for the Hénon attractor its measure theoretic entropy should be equal to its characteristic exponent. This result is known to be true for systems which satisfy Smale's Axiom A. In this article we report the results of our computations which suggest that Ruelle's conjecture may be true for the Hénon attractor. Further, in our study we are confronted with fundamental questions which suggest that certain existence theorems from ergodic theory are not sufficient from a computational point of view. |
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Keywords: | Characteristic exponent entropy partition |
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