New Discretization of Complex Analysis: The Euclidean and Hyperbolic Planes

Details New Discretization of Complex Analysis: The Euclidean and Hyperbolic Planes New Discretization of Complex Analysis: The Euclidean and Hyperbolic Planes

2008-09-17

arxiv.org/abs/0809.2963v2

Mathematics

Geometric Topology

16 pages, 12 figures, latex

Scientific paper

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 dynamics

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