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Numerical estimates of local dimension by waiting time and quantitative recurrence

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  • Carletti, Timoteo
  • Galatolo, Stefano

Abstract

Waiting time indicators are defined by measuring the time needed for a point x to approach a given point y. Our aim is to test the use of waiting time indicators, and quantitative recurrence ones to numerically estimate the local dimension of attractors in dynamical systems, as suggested by some rigorous results.

Suggested Citation

  • Carletti, Timoteo & Galatolo, Stefano, 2006. "Numerical estimates of local dimension by waiting time and quantitative recurrence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 120-128.
    • Handle: RePEc:eee:phsmap:v:364:y:2006:i:c:p:120-128
    DOI: 10.1016/j.physa.2005.10.003
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    References listed on IDEAS

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    1. Martı́nez-López, F. & Cabrerizo-Vı́lchez, M.A. & Hidalgo-Álvarez, R., 2001. "An improved method to estimate the fractal dimension of physical fractals based on the Hausdorff definition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 387-399.
    2. Thomas C. Halsey & Mogens H. Jensen, 2004. "Hurricanes and butterflies," Nature, Nature, vol. 428(6979), pages 127-128, March.
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