p-adic Differential Equations

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Focusing on p-adic differential equations, this second edition offers an in-depth exploration starting from foundational concepts to advanced research topics. It draws connections to classical ordinary differential equations and includes original findings significant to p-adic geometry and related fields. The updated text features five new chapters that broaden the understanding of solution convergence, introducing concepts like Berkovich analytification and convergence polygons, along with a global index theorem linked to the Laplacian of these polygons.