Theoretical analysis shows that arithmetic degrees relate to cohomological Lyapunov multipliers, supporting the Mordell--Lang conjecture.
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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Song et al. (2025) studied this question.
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