Recurrence and return times of the Sierpinski carpet |
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Authors: | Dominique Simpelaere |
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Institution: | (1) Laboratoire de Probabilités, Université Pierre et Marie Curie Paris VI, 75252 Paris Cedex 05, France |
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Abstract: | We compute the limit distribution of the recurrence and of the normalizedk th return times to small sets of the Sierpinski carpet with respect to a natural measure defined on it. It is proved that this dynamical system follows the Poisson law, as one could have expected for such schemes. We study different sequences which converge in finite distribution to the Poisson point process. This limit in law is very interesting in ergodic theory, and it seems to appear for chaotic dynamical systems such as the one we study. |
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Keywords: | Fractal thermodynamic formalism recurrence return times Poisson law |
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