A Memoir on Integrable Systems

Yuri Fedorov, Valerij Vasilievich Kozlov (Autoren)

Buch | Hardcover

2023 | 1st ed. 2023
Springer Berlin (Verlag)
978-3-540-59000-2 (ISBN)

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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.

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

Erscheint lt. Verlag	11.1.2023
Reihe/Serie	Springer Monographs in Mathematics
Übersetzer	Yu. Fedorov
Zusatzinfo	Approx. 280 p. 40 illus.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Abelian varieties • Dynamisches System • Dynamische Systeme • Hamiltonsches System • Integrable Systems • Integralrechnung • Lax pairs • tensor invariants • theta-functions
ISBN-10	3-540-59000-5 / 3540590005
ISBN-13	978-3-540-59000-2 / 9783540590002
Zustand	Neuware