ar X iv : 0 90 8 . 45 75 v 1 [ nl in . C D ] 3 1 A ug 2 00 9 FIRST POINCARÉ RETURNS , NATURAL MEASURE , UPOS AND KOLMOGOROV - SINAI ENTROPY

It is known that unstable periodic orbits of a given map give information about the natural measure of a chaotic attractor. In this work we show how these orbits can be used to calculate the density function of the first Poincaré returns. The close relation between periodic orbits and the Poincaré returns allows for analytical and semi-analytical estimations of relevant quantities in dynamical systems, as the decay of correlation and the Kolmogorov-Sinai entropy, in terms of this density function. Since return times can be trivially observed and measured, our approach is highly oriented to the treatment of experimental systems.