Entropy of holomorphic and rational maps: a survey

Shmuel Friedland

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Entropy of holomorphic and rational maps: a survey

Shmuel Friedland

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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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Shmuel Friedland. 2006-07-25. Entropy of holomorphic and rational maps: a survey. https://arxiv.org/abs/math/0605651

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