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Entropy of Meromorphic Maps and Dynamics of Birational Maps
Henry De Thélin, Université Paris 13, Villetaneuse, France, and Gabriel Vigny, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Amiens, France
A publication of the Société Mathématique de France.
Mémoires de la Société Mathématique de France
2011; 98 pp; softcover
Number: 122
ISBN-10: 2-85629-302-6
ISBN-13: 978-2-85629-302-7
List Price: US$42
Member Price: US$33.60
Order Code: SMFMEM/122
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The authors study the dynamics of meromorphic maps for a compact Kahler manifold \(X\). More precisely, they give a simple criterion that allows them to produce a measure of maximal entropy. They can apply this result to bound the Lyapunov exponents.

The authors then study the particular case of a family of generic birational maps of \(\mathbb{P} ^k\) for which they construct the Green currents and the equilibrium measure. They use for that the theory of super-potentials. They show that the measure is mixing and gives no mass to pluripolar sets. Using the criterion they get that the measure is of maximal entropy. This implies finally that the measure is hyperbolic.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in analysis.

Table of Contents

  • Introduction
  • Entropy of meromorphic maps
  • Dynamics of birational maps of \(\mathbb{P}^k\)
  • Super-potentials
  • Bibliography
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