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9781470450380 Academic Inspection Copy

Discrete Painleve Equations

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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.
Nalini Joshi, University of Sydney, Australia.
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.
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