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Papers by GARIN FEDOR JANAMPA AÑAÑOS

Research paper thumbnail of Media de Ensambles y la No Extensividad en el Borde del Caos: Mapa de Kaplan-Yorke

Anales Científicos, 2017

son estudiadas numéricamente, por medio de medias de ensambles, la sensibilidad a las condiciones... more son estudiadas numéricamente, por medio de medias de ensambles, la sensibilidad a las condiciones iniciales y la producción de la entropía por unidad de tiempo del mapa disipativo bidemsional de Kaplan-Yorke para dos casos: caos fuerte y caos débil (en el borde del caos). Se verifica que las propiedades de la sensibilidad y la producción de la entropía están relacionadas a un mismo valor del índice entrópico: q=1 para el caos fuerte y q<1 para el caos débil.

Research paper thumbnail of Edge of chaos of logistic-like maps: Sensitivity to the initial conditions and relaxation

We consider nonequilibrium probabilistic dynamics in logistic-like maps xt+1 = 1−a|xt| z , (z > 1... more We consider nonequilibrium probabilistic dynamics in logistic-like maps xt+1 = 1−a|xt| z , (z > 1) at their chaos threshold: We first introduce many initial conditions within one among W >> 1 intervals partitioning the phase space and focus on the unique value qsen < 1 for which the entropic form Sq ≡ 1− W i=1 p q i q−1 linearly increases with time. We then verify that Sq sen (t) − Sq sen (∞) vanishes like t −1/[q rel (W)−1] [q rel (W) > 1]. We finally exhibit a new finite-size scaling, q rel (∞) − q rel (W) ∝ W −|qsen|. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.

Research paper thumbnail of Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos

Physical Review Letters, 2002

We consider nonequilibrium probabilistic dynamics in logisticlike maps x t1 1 ÿ ajx t j z , z > 1... more We consider nonequilibrium probabilistic dynamics in logisticlike maps x t1 1 ÿ ajx t j z , z > 1 at their chaos threshold: We first introduce many initial conditions within one among W 1 intervals partitioning the phase space and focus on the unique value q sen < 1 for which the entropic form S q 1 ÿ P W i1 p q i =q ÿ 1 linearly increases with time. We then verify that S q sen t ÿ S q sen 1 vanishes like t ÿ1=q rel Wÿ1 [q rel W > 1]. We finally exhibit a new finite-size scaling, q rel 1 ÿ q rel W / W ÿjq sen j. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.

Research paper thumbnail of Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach

The European Physical Journal B, 2005

We perform a throughout numerical study of the average sensitivity to initial conditions and entr... more We perform a throughout numerical study of the average sensitivity to initial conditions and entropy production for two symplectically coupled standard maps focusing on the control-parameter region close to regularity. Although the system is ultimately strongly chaotic (positive Lyapunov exponents), it first stays lengthily in weak-chaotic regions (zero Lyapunov exponents). We argue that the nonextensive generalization of the classical formalism is an adequate tool in order to get nontrivial information about this complex phenomenon. Within this context we analyze the relation between the power-law sensitivity to initial conditions and the entropy production.

Research paper thumbnail of Generalization of the Kolmogorov–Sinai entropy: logistic-like and generalized cosine maps at the chaos threshold

Physics Letters A, 2001

We numerically calculate, at the edge of chaos, the time evolution of the nonextensive entropic f... more We numerically calculate, at the edge of chaos, the time evolution of the nonextensive entropic form Sq ≡ [1 − W i=1 p q i ]/[q − 1] (with S1 = − W i=1 pi ln pi) for two families of one-dimensional dissipative maps, namely a logistic-and a periodic-like with arbitrary inflexion z at their maximum. At t = 0 we choose N initial conditions inside one of the W small windows in which the accessible phase space is partitioned; to neutralize large fluctuations we conveniently average over a large amount of initial windows. We verify that one and only one value q * < 1 exists such that the limt→∞ limW →∞ limN→∞ Sq(t)/t is finite, thus generalizing the (ensemble version of) Kolmogorov-Sinai entropy (which corresponds to q * = 1 in the present formalism). This special, z-dependent, value q * numerically coincides, for both families of maps and all z, with the one previously found through two other independent procedures (sensitivity to the initial conditions and multifractal f (α) function).

Research paper thumbnail of Ensemble Averages and Nonextensivity at the Edge of Chaos of One-Dimensional Maps

Physical Review Letters, 2004

Ensemble averages of the sensitivity to initial conditions ξ(t) and the entropy production per un... more Ensemble averages of the sensitivity to initial conditions ξ(t) and the entropy production per unit time of a new family of one-dimensional dissipative maps, xt+1 = 1 − ae −1/|xt| z (z > 0), and of the known logistic-like maps, xt+1 = 1 − a|xt| z (z > 1), are numerically studied, both for strong (Lyapunov exponent λ1 > 0) and weak (chaos threshold, i.e., λ1 = 0) chaotic cases. In all cases we verify that (i) both lnq ξ [lnq x ≡ (x 1−q − 1)/(1 − q); ln1 x = ln x] and Sq [Sq ≡ (1 − i p q i)/(q − 1); S1 = − i pi ln pi] linearly increase with time for (and only for) a special value of q, q av sen , and (ii) the slope of lnq ξ and that of Sq coincide, thus interestingly extending the well known Pesin theorem. For strong chaos, q av sen = 1, whereas at the edge of chaos, q av sen (z) < 1.

Research paper thumbnail of Ensemble Averages and Nonextensivity at the Edge of Chaos of One-Dimensional Maps

Physical Review Letters, 2004

Research paper thumbnail of Media de Ensambles y la No Extensividad en el Borde del Caos: Mapa de Kaplan-Yorke

Anales Científicos, 2017

son estudiadas numéricamente, por medio de medias de ensambles, la sensibilidad a las condiciones... more son estudiadas numéricamente, por medio de medias de ensambles, la sensibilidad a las condiciones iniciales y la producción de la entropía por unidad de tiempo del mapa disipativo bidemsional de Kaplan-Yorke para dos casos: caos fuerte y caos débil (en el borde del caos). Se verifica que las propiedades de la sensibilidad y la producción de la entropía están relacionadas a un mismo valor del índice entrópico: q=1 para el caos fuerte y q<1 para el caos débil.

Research paper thumbnail of Edge of chaos of logistic-like maps: Sensitivity to the initial conditions and relaxation

We consider nonequilibrium probabilistic dynamics in logistic-like maps xt+1 = 1−a|xt| z , (z > 1... more We consider nonequilibrium probabilistic dynamics in logistic-like maps xt+1 = 1−a|xt| z , (z > 1) at their chaos threshold: We first introduce many initial conditions within one among W >> 1 intervals partitioning the phase space and focus on the unique value qsen < 1 for which the entropic form Sq ≡ 1− W i=1 p q i q−1 linearly increases with time. We then verify that Sq sen (t) − Sq sen (∞) vanishes like t −1/[q rel (W)−1] [q rel (W) > 1]. We finally exhibit a new finite-size scaling, q rel (∞) − q rel (W) ∝ W −|qsen|. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.

Research paper thumbnail of Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos

Physical Review Letters, 2002

We consider nonequilibrium probabilistic dynamics in logisticlike maps x t1 1 ÿ ajx t j z , z > 1... more We consider nonequilibrium probabilistic dynamics in logisticlike maps x t1 1 ÿ ajx t j z , z > 1 at their chaos threshold: We first introduce many initial conditions within one among W 1 intervals partitioning the phase space and focus on the unique value q sen < 1 for which the entropic form S q 1 ÿ P W i1 p q i =q ÿ 1 linearly increases with time. We then verify that S q sen t ÿ S q sen 1 vanishes like t ÿ1=q rel Wÿ1 [q rel W > 1]. We finally exhibit a new finite-size scaling, q rel 1 ÿ q rel W / W ÿjq sen j. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.

Research paper thumbnail of Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach

The European Physical Journal B, 2005

We perform a throughout numerical study of the average sensitivity to initial conditions and entr... more We perform a throughout numerical study of the average sensitivity to initial conditions and entropy production for two symplectically coupled standard maps focusing on the control-parameter region close to regularity. Although the system is ultimately strongly chaotic (positive Lyapunov exponents), it first stays lengthily in weak-chaotic regions (zero Lyapunov exponents). We argue that the nonextensive generalization of the classical formalism is an adequate tool in order to get nontrivial information about this complex phenomenon. Within this context we analyze the relation between the power-law sensitivity to initial conditions and the entropy production.

Research paper thumbnail of Generalization of the Kolmogorov–Sinai entropy: logistic-like and generalized cosine maps at the chaos threshold

Physics Letters A, 2001

We numerically calculate, at the edge of chaos, the time evolution of the nonextensive entropic f... more We numerically calculate, at the edge of chaos, the time evolution of the nonextensive entropic form Sq ≡ [1 − W i=1 p q i ]/[q − 1] (with S1 = − W i=1 pi ln pi) for two families of one-dimensional dissipative maps, namely a logistic-and a periodic-like with arbitrary inflexion z at their maximum. At t = 0 we choose N initial conditions inside one of the W small windows in which the accessible phase space is partitioned; to neutralize large fluctuations we conveniently average over a large amount of initial windows. We verify that one and only one value q * < 1 exists such that the limt→∞ limW →∞ limN→∞ Sq(t)/t is finite, thus generalizing the (ensemble version of) Kolmogorov-Sinai entropy (which corresponds to q * = 1 in the present formalism). This special, z-dependent, value q * numerically coincides, for both families of maps and all z, with the one previously found through two other independent procedures (sensitivity to the initial conditions and multifractal f (α) function).

Research paper thumbnail of Ensemble Averages and Nonextensivity at the Edge of Chaos of One-Dimensional Maps

Physical Review Letters, 2004

Ensemble averages of the sensitivity to initial conditions ξ(t) and the entropy production per un... more Ensemble averages of the sensitivity to initial conditions ξ(t) and the entropy production per unit time of a new family of one-dimensional dissipative maps, xt+1 = 1 − ae −1/|xt| z (z > 0), and of the known logistic-like maps, xt+1 = 1 − a|xt| z (z > 1), are numerically studied, both for strong (Lyapunov exponent λ1 > 0) and weak (chaos threshold, i.e., λ1 = 0) chaotic cases. In all cases we verify that (i) both lnq ξ [lnq x ≡ (x 1−q − 1)/(1 − q); ln1 x = ln x] and Sq [Sq ≡ (1 − i p q i)/(q − 1); S1 = − i pi ln pi] linearly increase with time for (and only for) a special value of q, q av sen , and (ii) the slope of lnq ξ and that of Sq coincide, thus interestingly extending the well known Pesin theorem. For strong chaos, q av sen = 1, whereas at the edge of chaos, q av sen (z) < 1.

Research paper thumbnail of Ensemble Averages and Nonextensivity at the Edge of Chaos of One-Dimensional Maps

Physical Review Letters, 2004