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Please use this identifier to cite or link to this item: http://repositorio.ufba.br/ri/handle/ri/13039

Title: Entropy and Poincaré recurrence from a geometrical viewpoint
Other Titles: Nonlinearity
Authors: Varandas, Paulo César Rodrigues Pinto
Issue Date: 2009
Abstract: We study Poincaré recurrence from a purely geometrical viewpoint. In (Downarowicz and Weiss 2004 Illinois J. Math. 48 59–69) it was proven that the metric entropy is given by the exponential growth rate of return times to dynamical balls. Here we use combinatorial arguments to provide an alternative and more direct proof of this result and to prove that minimal return times to dynamical balls grow linearly with respect to its length. Some relations using weighted versions of recurrence times are also obtained for equilibrium states. Then we establish some interesting relations between recurrence, dimension, entropy and Lyapunov exponents of ergodic measures.
Description: Texto completo: acesso restrito. p. 2365-2375
URI: http://www.repositorio.ufba.br/ri/handle/ri/13039
ISSN: 0951-7715
Appears in Collections:Artigos Publicados em Periódicos (IM)

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