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Descripción
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| We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of maps introduced by C. Moore [Phys Rev Lett {\bf 64}, 2354 (1990)] in the context of undecidability. We calculated the time evolution of the entropy $S_q \equiv \frac{1-\sum_{i=1}^Wp_i^q}{q-1}$ ($S_1=S_{BG}\equiv -\sum_{i=1}^Wp_i \ln p_i$), and exhibited the dramatic effect introduced by numerical precision. Indeed, in spite of being area-preserving maps, they present, {\it well after} the initially concentrated ensemble has spread virtually all over the phase space, unexpected {\it pseudo-attractors} (fixed-point like for the baker map, and more complex structures for the Moore map). These pseudo-attractors, and the apparent time (partial) reversibility they provoke, gradually disappear for increasingly large precision. In the case of the Moore map, they are related to zero Lebesgue-measure effects associated with the frontiers existing in the definition of the map. In addition to the above, and consistently with the results by V. Latora and M. Baranger [Phys. Rev. Lett. {\bf 82}, 520 (1999)], we find that the rate of the far-from-equilibrium entropy production of baker map, numerically coincides with the standard Kolmogorov-Sinai entropy of this strongly chaotic system | |
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Internacional
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No |
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JCR del ISI
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No |
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Título de la revista
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Physica A |
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ISSN
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0378-4371 |
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Factor de impacto JCR
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0 |
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Información de impacto
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Volumen
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2 |
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DOI
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Número de revista
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386 |
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