Arithmetic Degrees are Cohomological Lyapunov Multipliers

2025/07/23 by Jiarui Song, Junyi Xie, Song, Jiarui +2
Computer Science · Engineering · Mathematics · #37P05 #37P30 #Algebraic Geometry (math.AG) #Computability, Logic, AI Algorithms #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2507.17643

openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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Related

• Arithmetic degrees and dynamical degrees of endomorphisms on surfaces
• Arithmetic degree and its application to Zariski dense orbit conjecture
• Arithmetic degrees and Zariski dense orbits of cohomologically hyperbolic maps
• Examples of dynamical degree equals arithmetic degree
• Height arguments toward the dynamical Mordell-Lang problem in arbitrary characteristic