For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the irreversibility of the map. We indicate how it can be exactly calculated.
Postal address: Laboratoire de Physique Théorique et des Hautes EnergiesUniversité Pierre et Marie Curie, boîte postale 126.
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