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arXiv · 2507.17643

Arithmetic Degrees are Cohomological Lyapunov Multipliers

Jiarui Song·Junyi Xie·She Yang
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Abstract

For endomorphisms of projective varieties, we prove that the arithmetic degree of a point with Zariski dense orbit must be a cohomological Lyapunov multiplier of the dynamical system. We will apply our result to deduce a corollary towards the dynamical Mordell--Lang conjecture.

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Jiarui Song, Junyi Xie, She Yang. 2025-07-23. Arithmetic Degrees are Cohomological Lyapunov Multipliers. https://arxiv.org/abs/2507.17643

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