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Symmetries and related topics in differential and difference equations : Jairo Charris Seminar 2009, Symmetries of Differential and Difference Equations, Escuela de Matemáticas, Universidad Sergio Arboleda, Bogotá, Colombia / David Blázquez-Sanz, Juan J. Morales-Ruiz, Jesús Rodríguez Lombardero, editors.
- Format:
- Book
- Conference/Event
- Author/Creator:
- Jairo Charris Seminar, Corporate Author.
- Conference Name:
- Jairo Charris Seminar (2009 : Universidad Sergio Arboleda), issuing body.
- Jairo Charris Seminar.
- Series:
- Contemporary mathematics, 0271-4132 549
- Contemporary mathematics, 549 0271-4132
- Language:
- English
- Subjects (All):
- Symmetry (Mathematics)--Congresses.
- Symmetry (Mathematics).
- Difference equations--Congresses.
- Difference equations.
- Differential-algebraic equations--Congresses.
- Differential-algebraic equations.
- Physical Description:
- 1 online resource (178 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society ; [Bogotá, Colombia] : Instituto de Matemáticas y sus Aplicaciones, [2011]
- Language Note:
- English
- Summary:
- This volume represents the 2009 Jairo Charris Seminar in Symmetries of Differential and Difference Equations, which was held at the Universidad Sergio Arboleda in Bogota, 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 Matematicas y sus Aplicaciones (IMA).
- Contents:
- Contents
- Jairo Charris, The mathematician, The seminar
- Preface
- A reduction method for higher order variational equations of Hamiltonian systems
- A survey on integration of parabolic equations by reducing them to the heat equation
- 1. Introduction
- 2. Reduction by transformation (1.2)
- 3. Applications of Theorem 2.1
- 4. Reduction by general equivalence transformation
- References
- Weil jets, Lie correspondences and applications
- Introduction
- 1. Jets of submanifolds
- 2. Lie correspondences between jet spaces
- 3. Prolongations and correspondences.
- 4. Characteristics, singular vector fields and correspondences
- 5. Symmetries and Lie correspondences
- 6. Projections, transversality and the process of reduction by symmetries
- Acknowledgments
- Some applications of summability: An illustrated survey
- The structure of time and inertial forces in Lagrangian mechanics
- 0. Notations and definitions
- 1. Structure of a second order differential equation relative to a metric
- 2. Newton-Lagrange mechanics of a free system
- 3. Constrained systems
- 4. The class of time and the calculus of variations
- 5. Time constraints
- 6. Modification caused by a time constraint in a free system
- 7. Linear constraints depending on time
- 8. Reference frames and inertial forces
- Acknowledgements.
- Differential invariant algebras
- 1. Introduction.
- 2. Moving Frames and Differential Invariants.
- 3. Equivariant Moving Frames.
- 4. Recurrence.
- 5. Generating Invariants.
- 6. Differential Invariant Algebras of Pseudo-Groups.
- The Stokes phenomenon for linear q-difference equations
- 2. Some background
- 3. Some examples around the q-Euler equation
- Finite Hamiltonian systems on phase space.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 0-8218-8228-7
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