Publication of "Symmetries and Related Topics in Differential and Difference Equations"

Edited by: David Blázquez-Sanz, Universidad Sergio Arboleda, Bogatá, Colombia, Juan J. Morales-Ruiz, Technical University of Madrid, Spain, and Jesús Rodríguez Lombardero, Universidad de Salamanca, Spain

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

• A. A. Monforte and J.-A. Weil -- A reduction method for higher order variational equations of Hamiltonian systems
• N. H. Ibragimov -- A survey on integration of parabolic equations by reducing them to the heat equation
• S. Jiménez -- Weil jets, Lie correspondences and applications
• J. Mozo-Fernández -- Some applications of summability: An illustrated survey
• J. M. Díaz -- The structure of time and inertial forces in Lagrangian mechanics
• P. J. Olver -- Differential invariant algebras
• J. Sauloy -- The Stokes phenomenon for linear $q$-difference equations
• K. B. Wolf -- Finite Hamiltonian systems on phase space