**Contemporary Mathematics**

Volume: 549;
2011;
163 pp;
Softcover

MSC: Primary 35; 34; 17; 70; 37; 22; 53; 39;

**Print ISBN: 978-0-8218-6872-0
Product Code: CONM/549**

List Price: $78.00

AMS Member Price: $62.40

MAA Member Price: $70.20

**Electronic ISBN: 978-0-8218-8228-3
Product Code: CONM/549.E**

List Price: $73.00

AMS Member Price: $58.40

MAA Member Price: $65.70

# Symmetries and Related Topics in Differential and Difference Equations

Share this page *Edited by *
*David Blázquez-Sanz; Juan J. Morales-Ruiz; Jesús Rodríguez Lombardero*

This volume represents the 2009 Jairo Charris Seminar in Symmetries of
Differential and Difference Equations, which was held at the
Universidad Sergio Arboleda in Bogotá, Colombia.

The papers include topics such as Lie symmetries, equivalence
transformations and differential invariants, group theoretical methods
in linear equations, namely differential Galois theory and Stokes
phenomenon, and the development of some geometrical methods in
theoretical physics.

The reader will find new interesting results in symmetries of
differential and difference equations, applications in classical and
quantum mechanics, two fundamental problems of theoretical mechanics,
the mathematical nature of time in Lagrangian mechanics and the
preservation of the equations of motion by changes of frame, and
discrete Hamiltonian systems arising in geometrical optics and
analogous to those of finite quantum mechanics.

This book is published in cooperation with Instituto de Matemáticas y sus Aplicaciones (IMA)

#### Readership

Graduate students and research mathematicians interested in using symmetries in various areas of analysis.

# Table of Contents

## Symmetries and Related Topics in Differential and Difference Equations

- Contents v6 free
- Jairo Charris, The mathematician, The seminar vii8 free
- Preface ix10 free
- A reduction method for higher order variational equations of Hamiltonian systems 112 free
- A survey on integration of parabolic equations by reducing them to the heat equation 1728
- Weil jets, Lie correspondences and applications 2536
- Introduction 2637
- 1. Jets of submanifolds 2738
- 2. Lie correspondences between jet spaces 3142
- 3. Prolongations and correspondences. 3647
- 4. Characteristics, singular vector fields and correspondences 3950
- 5. Symmetries and Lie correspondences 4354
- 6. Projections, transversality and the process of reduction by symmetries 4758
- Acknowledgments 4960
- References 4960

- Some applications of summability: An illustrated survey 5162
- The structure of time and inertial forces in Lagrangian mechanics 6576
- Introduction 6576
- 0. Notations and definitions 6677
- 1. Structure of a second order differential equation relative to a metric 6879
- 2. Newton-Lagrange mechanics of a free system 7283
- 3. Constrained systems 7384
- 4. The class of time and the calculus of variations 7788
- 5. Time constraints 8192
- 6. Modification caused by a time constraint in a free system 8394
- 7. Linear constraints depending on time 8697
- 8. Reference frames and inertial forces 8899
- Acknowledgements. 93104
- References 93104

- Differential invariant algebras 95106
- The Stokes phenomenon for linear q-difference equations 123134
- Finite Hamiltonian systems on phase space 141152