**CBMS Regional Conference Series in Mathematics**

Volume: 131;
2019;
146 pp;
Softcover

MSC: Primary 33; 39; 14; 32;

Print ISBN: 978-1-4704-5038-0

Product Code: CBMS/131

List Price: $55.00

AMS Member Price: $44.00

MAA Member Price: $49.50

**Electronic ISBN: 978-1-4704-5235-3
Product Code: CBMS/131.E**

List Price: $55.00

AMS Member Price: $44.00

MAA Member Price: $49.50

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#### Supplemental Materials

# Discrete Painlevé Equations

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*Nalini Joshi*

A co-publication of the AMS and CBMS

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.

#### Readership

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.

#### Table of Contents

# Table of Contents

## Discrete Painleve Equations

- Cover Cover11
- Title page i2
- Preface v6
- Chapter 1. Introduction 18
- Chapter 2. A dynamical systems approach 1724
- Chapter 3. Initial value spaces 2532
- Chapter 4. Foliated initial value spaces 4552
- Chapter 5. Cremona mappings 5966
- Chapter 6. Asymptotic analysis 7582
- Chapter 7. Lax pairs 8794
- Chapter 8. Riemann-Hilbert problems 95102
- Appendix A. Foliations and vector bundles 105112
- Appendix B. Projective spaces 107114
- Appendix C. Reflection groups 115122
- Appendix D. Lists of discrete Painlevé equations 119126
- Appendix E. Asymptotics of discrete equations 125132
- Bibliography 137144
- Index 145152
- Back Cover Back Cover1154