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Full Description
Discrete Painleve equations are nonlinear difference equations, which arise from translations on crystallographic lattices. The deceptive simplicity of this statement hides immensely rich mathematical properties, connecting dynamical systems, algebraic geometry, Coxeter groups, topology, special functions theory, and mathematical physics.
This book necessarily starts with introductory material to give the reader an accessible entry point to this vast subject matter. It is based on lectures that the author presented as principal lecturer at a Conference Board of Mathematical Sciences and National Science Foundation conference in Texas in 2016. Instead of technical theorems or complete proofs, the book relies on providing essential points of many arguments through explicit examples, with the hope that they will be useful for applied mathematicians and physicists.
Contents
Introduction
A dynamical systems approach
Initial value spaces
Foliated initial value spaces
Cremona mappings
Asymptotic analysis
Lax pairs
Riemann-Hilbert problems
Foliations and vector bundles
Projective spaces
Reflection groups
Lists of discrete-Painleve equations
Asymptotics of discrete equations
Bibliography
Index.
