Convergence to the critical attractor of dissipative maps: Log-periodic oscillations, fractality, and nonextensivity


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DE MOURA F., Tirnakli U. , LYRA M.

PHYSICAL REVIEW E, cilt.62, ss.6361-6365, 2000 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 62 Konu: 5
  • Basım Tarihi: 2000
  • Doi Numarası: 10.1103/physreve.62.6361
  • Dergi Adı: PHYSICAL REVIEW E
  • Sayfa Sayısı: ss.6361-6365

Özet

For a family of logisticlike maps, we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space. We found that the phase-space volume occupied by the ensemble W(t) depicts a power-law decay with log-periodic oscillations reflecting the multifractal character of the critical attractor. We explore the parametric dependence of the power-law exponent and the amplitude of the log-periodic oscillations with the attractor's fractal dimension governed by the inflection of the map near its extremal point. Further, we investigate the temporal evolution of W(t) for the circle map whose critical attractor is dense. In this case, we found W(t) to exhibit a rich pattern with a slow logarithmic decay of the lower bounds. These results are discussed in the context of nonextensive Tsallis entropies.