Conditional entropy - A tool to explore the phase space

In this paper we show that the Conditional Entropy of nearby orbits may be a useful tool to explore the phase space associated to a given Hamiltonian. The arc length parameter along the orbits, instead of the time, is used as a random variable to compute the entropy. In the first part of this work w e summarise the main analytical results to support this tool while, in the second part, we present numerical evidence that this technique is able to l ocalise (stable) periodic and quasiperiodic orbits, 'aperiodic' orbits (cha otic motion) and unstable periodic orbits (the 'source' of chaotic motion). Besides, we show that this technique provides a measure of chaos which is similar to that given by the largest Lyapunov Characteristic Number. It is important to remark that this method is very simple to compute and does not require long time integrations, just realistic physical times.