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It is known that unstable periodic orbits of a given map give informationabout the natural measure of a chaotic attractor. In this work we show howthese orbits can be used to calculate the density function of the firstPoincar\'e returns. The close relation between periodic orbits and thePoincar\'e returns allows for estimates of relevant quantities in dynamicalsystems, as the Kolmogorov-Sinai entropy, in terms of this density function.Since return times can be trivially observed and measured, our approach tocalculate this entropy is highly oriented to the treatment of experimentalsystems. We also develop a method for the numerical computation of unstableperiodic orbits.

Density of first Poincar\'e returns, periodic orbits, and Kolmogorov-Sinai entropy