January  2002, 8(1): 137-146. doi: 10.3934/dcds.2002.8.137

Dynamically defined recurrence dimension

1. 

Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic

2. 

PHYMAT, Université de Toulon et du Var, Centre de Physique Théorique, Luminy, France, France

Received  August 2000 Revised  July 2001 Published  October 2001

We modify the idea of a previous article [8] and introduce polynomial and exponential dynamically defined recurrence dimensions, topological invariants which express how the Poincaré recurrence time of a set grows when the diameter of the set shrinks. We introduce also the concept of polynomial entropy which applies in the case that topological entropy is zero and complexity function is polynomial. We compare recurrence dimensions with topological and polynomial entropies, evaluate recurrence dimensions of Sturmian subshifts and show some examples with Toeplitz subshifts.
Citation: Petr Kůrka, Vincent Penné, Sandro Vaienti. Dynamically defined recurrence dimension. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 137-146. doi: 10.3934/dcds.2002.8.137
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