A Memoir on Integrable Systems

Integrable dynamical systems are usually associated with Hamiltonian ones. The present book considers the bigger class of systems which are not (at least a priori) Hamiltonian but possess tensor invariants, in particular, an invariant measure. Such systems are as rare as Hamiltonian ones that have additional first integrals and therefore must be considered as number one candidates for integrable problems. Several integrability theorems related to the existence of tensor invariants are formulated. The authors display the geometrical background of some classical and new hierarchies of integrable systems and give their explicit solution in terms of theta-functions.
Most of the results discussed in this book have not been published before, so that this book will be immensely useful both to specialists in analytical dynamics who are interested in integrable problems and those in algebraic geometry who are looking for applications.

List of contents

Classical Mechanics and Lie Groups.- Systems With an Invariant Measure.- Integrable Systems, Lax Pairs and Confocal Quadrics.- Explicit Solutions.- References.- Index.

Summary

Integrable dynamical systems are usually associated with Hamiltonian ones. The present book considers the bigger class of systems which are not (at least a priori) Hamiltonian but possess tensor invariants, in particular, an invariant measure. Such systems are as rare as Hamiltonian ones that have additional first integrals and therefore must be considered as number one candidates for integrable problems. Several integrability theorems related to the existence of tensor invariants are formulated. The authors display the geometrical background of some classical and new hierarchies of integrable systems and give their explicit solution in terms of theta-functions.
Most of the results discussed in this book have not been published before, so that this book will be immensely useful both to specialists in analytical dynamics who are interested in integrable problems and those in algebraic geometry who are looking for applications.

Product details

• Authors: Yu. N. Fedorov, Yur Fedorov, Yuri Fedorov, V. V. Kozlov, Valerij Vasilievich Kozlov
• Assisted by: Yu Fedorov (Translation), Yu. Fedorov (Translation)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.01.2019
• EAN: 9783540590002
• ISBN: 978-3-540-59000-2
• No. of pages: 280
• Illustrations: Approx. 280 p. 40 illus.
• Series: Springer Monographs in Mathematics; Schriftenreihe Markt und Marketing; Springer Monographs in Mathematics; Schriftenreihe Markt und Marketing
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, B, Mathematics and Statistics, Algebraic Geometry, Theoretical, Mathematical and Computational Physics, Mathematical physics, Numerical analysis, Topological Groups, Lie Groups, Manifolds (Mathematics), Topological groups, Lie groups, Topological Groups and Lie Groups, Groups & group theory, Analysis (Mathematics), Mathematical analysis, Global analysis (Mathematics), Global Analysis and Analysis on Manifolds