Tropical Dynamics of Area-Preserving Maps
Simion Filip
TL;DR
This paper studies a class of area-preserving, piecewise affine maps on the 2-sphere, linking tropical and Berkovich geometries to automorphisms of degenerating K3 surfaces.
Contribution
It introduces a novel approach to analyze automorphisms of K3 surfaces using tropical and Berkovich geometric techniques.
Findings
Characterization of area-preserving maps on the 2-sphere
Connection between these maps and degenerating K3 surface automorphisms
Application of tropical geometry methods to complex surface dynamics
Abstract
We consider a class of area-preserving, piecewise affine maps on the 2-sphere. These maps encode degenerating families of K3 surface automorphisms and are profitably studied using techniques from tropical and Berkovich geometries.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons