內容簡介
This volume contains five surveys odynamical systems. The first one deals with nonholonomic mechanics and gives aupdated and systematic treatment of the geometry of distributions and of variational problems with nonintegrable constraints. The moderlanguage of differential geometry used throughout the survey allows for a clear and unified expositioof the earlier work ononholonomic problems. There is a detailed discussioof the dynamical properties of the nonholonomic geodesic flow and of various related concepts, such as nonholonomic exponential mapping, nonholonomic sphere, etc.
Other surveys treatvarious aspects of integrable Hamiltoniasystems, with aemphasis oLie-algebraic constructions. Among the topics covered are: the generalized Calogero-Moser systems based oroot systems of simple Lie algebras, a general r-matrix scheme for constructing integrable systems and Lax pairs, links with finite-gap integratiotheory, topological aspects ofintegrable systems, integrable tops, etc. One of the surveys gives a thorough analysis of a family of quantum integrable systems(Toda lattices)using the machinery of representatiotheory.
Readers will find all the new differential geometric and Liealgebraic methods which are currently used ithe theory of integrable systems ithis book. It will be indispensable to graduate students and researchers imathematics and theoretical physics.
Other surveys treatvarious aspects of integrable Hamiltoniasystems, with aemphasis oLie-algebraic constructions. Among the topics covered are: the generalized Calogero-Moser systems based oroot systems of simple Lie algebras, a general r-matrix scheme for constructing integrable systems and Lax pairs, links with finite-gap integratiotheory, topological aspects ofintegrable systems, integrable tops, etc. One of the surveys gives a thorough analysis of a family of quantum integrable systems(Toda lattices)using the machinery of representatiotheory.
Readers will find all the new differential geometric and Liealgebraic methods which are currently used ithe theory of integrable systems ithis book. It will be indispensable to graduate students and researchers imathematics and theoretical physics.