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Explore the third lecture in a mathematical series examining conjectures about the geometry of preperiodic points for endomorphisms of $ \mathbb{P}^{N}$, focusing on families of maps on $\mathbb{P}^{N}$ and their relationship to dynamical stability. Delve into the dynamical version of the "Relative Manin-Mumford" theorem, originally proven by Gao-Habegger for abelian varieties, and discover its connections to moduli spaces of maps on $\mathbb{P}^{N}$. Learn from Professor Laura DeMarco's collaborative work with Myrto Mavraki, presented at the "Arithmetic, Algebraic and Analytics Dynamics" thematic meeting at CIRM in Marseille, France. Access this comprehensive mathematical discussion through CIRM's Audiovisual Mathematics Library, featuring chapter markers, keywords, enriched content with abstracts and bibliographies, and advanced search functionality for a customized learning experience.
