A Memoir on Integrable Systems

The book discusses the class of systems that are not Hamiltonian but possess tensor invariants, which are as rare as Hamiltonian systems with additional first integrals. It formulates integrability theorems related to the existence of tensor invariants and provides explicit solutions in terms of theta-functions. The results are useful for specialists in analytical dynamics and algebraic geometry.

Format: Hardback
Publication date: 11 January 2023
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Integrable dynamical systems are often linked to Hamiltonian ones. The present book explores a broader category of systems that do not necessarily possess a Hamiltonian structure, but do possess tensor invariants, specifically an invariant measure. These systems, while uncommon compared to Hamiltonian systems with additional first integrals, hold great potential for solving integrable problems. Several integrability theorems related to the presence of tensor invariants are formulated by the authors. They provide a geometrical background for classical and novel hierarchies of integrable systems, offering explicit solutions in terms of theta-functions.

Notably, most of the results presented in this book have not been previously published, making it an invaluable resource for both analytical dynamics specialists interested in integrable problems and algebraic geometry enthusiasts seeking applications. The book's comprehensive coverage and novel insights make it a must-read for scholars in these fields.

Dimension: 235 x 155 (mm)
ISBN-13: 9783540590002
Edition number: 1st ed. 2022