Entropy of holomorphic and rational maps: a survey

2006/05/24 by Friedland, Shmuel
#28D20 #30D05 #37F #54H20 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0605651

Abstract

We give a brief survey on the entropy of holomorphic self maps f of compact Kähler manifolds, and rational dominating self maps f of smooth projective varieties. We emphasize the connection between the entropy and the spectral radii of the induced action of f on the homology of the compact manifold. The main conjecture for the rational maps states that modulo birational isomorphism all various notions of entropy and the spectral radii are equal.

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