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

Guiomar Ruiz and Constantino Tsallis

Physica A: Statistical Mechanics and its Applications, 2007, vol. 386, issue 2, 720-728

Abstract: 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 Sq≡(1-∑i=1Wpiq)/(q-1) (S1=SBG≡-∑i=1Wpilnpi). 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.

Keywords: Nonlinear dynamics; Nonextensive statistical mechanics; Precision effects; Attractors; Weak chaos (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:386:y:2007:i:2:p:720-728

DOI: 10.1016/j.physa.2007.07.070

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