Arithmetic Degrees are Cohomological Lyapunov Multipliers

Key Points

• The arithmetic degree of points with Zariski dense orbit relates directly to cohomological Lyapunov multipliers, establishing a foundational result in dynamical systems.
• Our findings indicate the connection between arithmetic degrees and cohomological multipliers, enhancing understanding of dynamic behaviors in projective varieties.
• Application to the dynamical Mordell--Lang conjecture offers significant implications for future research in algebraic geometry and dynamical systems.
• The study contributes to the field by demonstrating this essential link, paving the way for further exploration of these mathematical concepts.