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arXiv · 2110.09986

Dimensional preimage entropies

Henry de Thelin
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Abstract

Let $X$ be a compact complex manifold of dimension $k$ and $f:X \longrightarrow X$ be a dominating meromorphic map. We generalize the notion of topological entropy, by defining a quantity $h_{(m,l)}^{top}(f)$ which measures the action of $f$ on local analytic sets $W$ of dimension $l$ with $W \subset f^{-n}(\Delta)$ where $\Delta$ is a local analytic set of dimension $m$. We give then inequalities between $h_{(m,l)}^{top}(f)$ and Lyapounov exponents of suitable invariant measures.

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Henry de Thelin. 2021-10-19. Dimensional preimage entropies. https://arxiv.org/abs/2110.09986

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