A Memoir on Integrable Systems

1. Auflage 2023
ISBN: 978-3-540-59000-2
Verlag: Springer-Verlag GmbH

Buch, Englisch, 280 Seiten, Format (B × H): 193 mm x 270 mm

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Fedorov, Yuri

Kozlov, Valerij Vasilievich

Weitere Mitwirkende

Fedorov, Yu.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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