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New Discretization of Complex Analysis: The Euclidean and Hyperbolic Planes
Few years ago we developed jointly with I.Dynnikov new discretization of
complex analysis (DCA) based on the two-dimensional manifolds with colored
black/white triangulation. Especially deep results were obtained for the
Euclidean plane with equilateral triangle lattice. In the present work we
develop a DCA theory for the analogs of equilateral triangle lattice in
Hyperbolic plane. Some specific very interesting "dynamical phenomena" appear
in this case solving most fundamental boundary problems. Mike Boyle from the
University of Maryland helped to use here the methods of symbolic dynamicsComment: 16 pages, 12 figures, late
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