Communications in Mathematical Physics

, Volume 204, Issue 2, pp 425-437

Algebraic Entropy

  • M. P. BellonAffiliated withLaboratoire de Physique Théorique et Hautes Energies, Unité Mixte de Recherche 7589, CNRS et¶Universités Paris VI et Paris VII, Paris, France
  • , C.-M. VialletAffiliated withLaboratoire de Physique Théorique et Hautes Energies, Unité Mixte de Recherche 7589, CNRS et¶Universités Paris VI et Paris VII, Paris, France

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Abstract:

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.