Symmetries and Related Topics in Differential and Difference Equations
About this Title
David Blázquez-Sanz, Universidad Sergio Arboleda, Bogatá, Colombia, Juan J. Morales-Ruiz, Technical University of Madrid, Madrid, Spain and Jesús Rodríguez Lombardero, Universidad de Salamanca, Salamanca, Spain, Editors
Publication: Contemporary Mathematics
Publication Year 2011: Volume 549
ISBNs: 978-0-8218-6872-0 (print); 978-0-8218-8228-3 (online)
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.
Graduate students and research mathematicians interested in using symmetries in various areas of analysis.
Table of Contents
- A. Aparicio 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
- Jorge Mozo-Fernández – Some applications of summability: An illustrated survey
- J. Muñoz Díaz – The structure of time and inertial forces in Lagrangian mechanics
- Peter J. Olver – Differential invariant algebras
- Jacques Sauloy – The Stokes phenomenon for linear $q$-difference equations
- Kurt Bernardo Wolf – Finite Hamiltonian systems on phase space