Roundoff-induced attractors and reversibility in conservative two-dimensional maps

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• 作者：Guiomar Ruiz ; Constantino Tsallis
• 关键词：Nonlinear dynamics ; Nonextensive statistical mechanics ; Precision effects ; Attractors ; Weak chaos
• 刊名：Physica A
• 出版年：2007
• 出版时间：15 December 2007
• 年：2007
• 卷：386
• 期：2
• 页码：720-728
• 全文大小：1169 K

文摘

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. 64 (1990) 2354] in the context of undecidability. We calculate the time evolution of the entropy (). We exhibit the dramatic effect introduced by numerical precision. Indeed, in spite of being area-preserving maps, they present, well after the initially concentrated ensemble has spread virtually all over the phase space, unexpected 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 consistent with the results by V. Latora and M. Baranger [Phys. Rev. Lett. 82 (1999) 520], 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.