Entropy of holomorphic and rational maps: a survey

Details Entropy of holomorphic and rational maps: a survey Entropy of holomorphic and rational maps: a survey

2006-05-24

arxiv.org/abs/math/0605651v3

Mathematics

Dynamical Systems

13 pages, revised version

Scientific paper

We give a brief survey on the entropy of holomorphic self maps $f$ of compact K\"ahler 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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