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math.DS2026
Integrability of Cauchy problems for discrete conformal maps and circle patterns
Maxim Arnold, Anton Izosimov
A map from a square lattice to the Riemann sphere is called discrete conformal if the image of every elementary square is a harmonic quadrilateral. We prove that the initial value…
math.DS2024
A family of maps and a vector field on plane polygons
Maxim Arnold, Lael Costa, Serge Tabachnikov
We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discre…