1,721,035 research outputs found
On time and ensemble averages in quasistationary state of low-dimensional Hamiltonian maps
No full textWe discuss the relation between ensemble and time averages for quasistationary states of low-dimensional symplectic maps that present remarkable analogies with similar states detected in many-body long-range-interacting Hamiltonian systems. (C) 2004 Elsevier B.V. All rights reserved
Routes to chaos, universality and glass formation
No full textWe review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these situations the dynamical behavior is exactly describable through infinite families of Tsallis' q-exponential functions. Furthermore, the addition of a noise perturbation to the dynamics at the onset of chaos of the logistic map allows to establish parallels with the behavior of supercooled liquids close to glass formation. Specifically, the occurrence of two-step relaxation, aging with its characteristic scaling property, and subdiffusion and arrest is corroborated for such a system
Efeitos dinamicos anomalos em sistemas de baixa dimensao e conexoes com a mecanica estatistica nao extensiva
No full textConduction at the onset of chaos
No full textAfter a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian particles, both analytically and numerically, and address then whether aspects of the classic Onsager's picture generalize to the non-local non-reversible dynamics described by logistic map iterates. While in the chaotic case numerical evidence of a monotonic relaxation is found, at the onset of chaos complex relaxation patterns emerge
Mixing and approach to equilibrium in the standard map
No full textFor a paradigmatic case, the standard map, we discuss how the statistical description of the approach to equilibrium is related to the sensitivity to the initial conditions of the system. Using a numerical analysis we present an anomalous scenario that may give some insight on the foundations of the Tsallis' statistical mechanics. (C) 2002 Elsevier Science B.V. All rights reserved
Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics
No full textWe uncover the dynamics at the chaos threshold mu(infinity) of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period-doubling cascade that occurs for mu<mu(infinity). We corroborate this structure analytically via the Feigenbaum renormalization-group (RG) transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential, of which we determine the q index and the q-generalized Lyapunov coefficient lambda(q). Our results are an unequivocal validation of the applicability of the nonextensive generalization of Boltzmann-Gibbs statistical mechanics to critical points of nonlinear maps
Numerical analysis of conservative maps: a possible foundation of nonextensive phenomena
No full textGlassy Dynamics at the Onset of Chaos with Additive Noise
No full textAfter recalling key phenomenological properties of glass formation, we point out that similar features are exhibited by the dynamical properties of the noise-perturbed iterates of the logistic map at the onset of chaos. The analysis includes two-step relaxation, aging, subdiffusion and arrest, as well as an expression analogous to the Adam-Gibbs relation connecting dynamical and thermodynamic properties of a glass former. The dynamical properties of the logistic map in the presence of external noise are seen to be comparable to those of a supercooled liquid above a glass transition temperature, whereas the noiseless attractor displays typical nonequilibrium aspects like loss of time translation invariance (aging). Reference is made to connections between the noiseless dynamics at the chaos threshold and the nonextensive formalism
Nonextensive Pesin identity: Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map
No full textWe show that the dynamical and entropic properties at the chaos threshold of the logistic map are naturally linked through the nonextensive expressions for the sensitivity to initial conditions and for the entropy. We corroborate analytically, with the use of the Feigenbaum renormalization group transformation, the equality between the generalized Lyapunov coefficient lambda(q) and the rate of entropy production, K(q), given by the nonextensive statistical mechanics. Our results advocate the validity of the q-generalized Pesin identity at critical points of one-dimensional nonlinear dissipative maps
Scaling and efficiency determine the irreversible evolution of a market
Full text linkIn setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable basis for simulating such series. Based on constraints imposed by market efficiency and on an inhomogeneous-time generalization of standard simple scaling, we propose an analytical model which accounts simultaneously for empirical results like the linear decorrelation of successive returns, the power law dependence on time of the volatility autocorrelation function, and the multiscaling associated to this dependence. in addition, our approach gives a justification and a quantitative assessment of the irreversible character of the index dynamics. This irreversibility enters as a key ingredient in a novel simulation strategy of index evolution which demonstrates the predictive potential of the model
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