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On the fractal dimension of orbits compatible with Tsallis statistics

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  • Carati, A.

Abstract

In a previous paper [A. Carati, Physica A 348 (2005) 110–120] it was shown how, for a dynamical system, the probability distribution function of sojourn-times in phase-space, defined in terms of the dynamical orbits (up to a given observation time), induces unambiguously a statistical ensemble in phase-space. In the present paper, the p.d.f. of the sojourn-times corresponding to a Tsallis ensemble is obtained (this, by the way, requires the solution of a problem of a general character, disregarded in paper [A. Carati, Physica A 348 (2005) 110–120]). In particular some qualitative properties, such as the fractal dimension, of the dynamical orbits compatible with the Tsallis ensembles are indicated.

Suggested Citation

  • Carati, A., 2008. "On the fractal dimension of orbits compatible with Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(7), pages 1491-1503.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:7:p:1491-1503
    DOI: 10.1016/j.physa.2007.09.037
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