Softcover ISBN:  9781470450380 
Product Code:  CBMS/131 
List Price:  $58.00 
MAA Member Price:  $52.20 
AMS Member Price:  $46.40 
eBook ISBN:  9781470452353 
Product Code:  CBMS/131.E 
List Price:  $58.00 
MAA Member Price:  $52.20 
AMS Member Price:  $46.40 
Softcover ISBN:  9781470450380 
eBook: ISBN:  9781470452353 
Product Code:  CBMS/131.B 
List Price:  $116.00 $87.00 
MAA Member Price:  $104.40 $78.30 
AMS Member Price:  $92.80 $69.60 
Softcover ISBN:  9781470450380 
Product Code:  CBMS/131 
List Price:  $58.00 
MAA Member Price:  $52.20 
AMS Member Price:  $46.40 
eBook ISBN:  9781470452353 
Product Code:  CBMS/131.E 
List Price:  $58.00 
MAA Member Price:  $52.20 
AMS Member Price:  $46.40 
Softcover ISBN:  9781470450380 
eBook ISBN:  9781470452353 
Product Code:  CBMS/131.B 
List Price:  $116.00 $87.00 
MAA Member Price:  $104.40 $78.30 
AMS Member Price:  $92.80 $69.60 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 131; 2019; 146 ppMSC: Primary 33; 39; 14; 32
Discrete Painlevé 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.
ReadershipGraduate students and researchers interested in integrable systems, mathematical physics, applied mathematics and special functions, as well as resolution of singularities, dynamical systems, and birational geometry.

Table of Contents

Chapters

Introduction

A dynamical systems approach

Initial value spaces

Foliated initial value spaces

Cremona mappings

Asymptotic analysis

Lax pairs

RiemannHilbert problems

Foliations and vector bundles

Projective spaces

Reflection groups

Lists of discretePainlevé equations

Asymptotics of discrete equations


Additional Material

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Discrete Painlevé 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.
Graduate students and researchers interested in integrable systems, mathematical physics, applied mathematics and special functions, as well as resolution of singularities, dynamical systems, and birational geometry.

Chapters

Introduction

A dynamical systems approach

Initial value spaces

Foliated initial value spaces

Cremona mappings

Asymptotic analysis

Lax pairs

RiemannHilbert problems

Foliations and vector bundles

Projective spaces

Reflection groups

Lists of discretePainlevé equations

Asymptotics of discrete equations