Two-dimensional dissipative maps at chaos threshold: Sensitivity to initial conditions and relaxation dynamics

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dc.creatorBorges, Ernesto P.
dc.creatorTirnakli, Ugur
dc.date2003-12-29
dc.date.accessioned2026-07-07T02:55:39Z
dc.date.available2026-07-07T02:55:39Z
dc.descriptionThe sensitivity to initial conditions and relaxation dynamics of two-dimensional maps are analyzed at the edge of chaos, along the lines of nonextensive statistical mechanics. We verify the dual nature of the entropic index for the Henon map, one ($q_{sen}<1$) related to its sensitivity to initial conditions properties, and the other, graining-dependent ($q_{rel}(W)>1$), related to its relaxation dynamics towards its stationary state attractor. We also corroborate a scaling law between these two indexes, previously found for $z$-logistic maps. Finally we perform a preliminary analysis of a linearized version of the Henon map (the smoothed Lozi map). We find that the sensitivity properties of all these $z$-logistic, Henon and Lozi maps are the same, $q_{sen}=0.2445...$
dc.descriptionCommunication at NEXT2003, Second Sardinian International Conference on News and Expectations in Thermostatistics, Villasimius (Cagliari) Italy, 21-28 September 2003. Submitted to Physica A. Elsevier Latex, 8 pages, 6 eps figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0312683
dc.identifierhttp://arxiv.org/abs/cond-mat/0312683
dc.identifierPhysica A 340 227--233 (2004)
dc.identifierdoi:10.1016/j.physa.2004.04.011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/23015
dc.subjectStatistical Mechanics
dc.titleTwo-dimensional dissipative maps at chaos threshold: Sensitivity to initial conditions and relaxation dynamics
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