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Explore the mathematical concept of dynamical degrees in this 49-minute conference talk by Jason Bell at the Centre International de Rencontres Mathématiques in Marseille, France. Delve into how the degree of a dominant rational map f: ℙⁿ → ℙⁿ is defined by the common degree of its homogeneous components, and how iterating this map creates a submultiplicative sequence deg(fⁿ) that converges to a value λ ≥ 1, known as the first dynamical degree. Gain insights into the significance of dynamical degrees in complex dynamics and examine a specific example of a birational self-map of ℙ³ where this dynamical degree is proven to be transcendental. This presentation covers joint work with Jeffrey Diller, Mattias Jonsson, and Holly Krieger, and was recorded during the thematic meeting "Galois differential Theories and transcendence" on February 18, 2025. The video includes chapter markers, keywords, abstracts, and bibliographies for enhanced navigation and learning.
