<p>This volume contains five surveys on dynamical systems. The first one deals with nonholonomic mechanics and gives an updated and systematic treatment of the geometry of distributions and of variational problems with nonintegrable constraints. The modern language of differential geometry used throughout the survey allows for a clear and unified exposition of the earlier work on nonholonomic problems. There is a detailed discussion of the dynamical properties of the nonholonomic geodesic flow and of various related concepts, such as nonholonomic exponential mapping, nonholonomic sphere, etc. Other surveys treat various aspects of integrable Hamiltonian systems, with an emphasis on Lie-algebraic constructions. Among the topics covered are: the generalized Calogero-Moser systems based on root systems of simple Lie algebras, a ge- neral r-matrix scheme for constructing integrable systems and Lax pairs, links with finite-gap integration theory, topological aspects of integrable 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 representation theory. Readers will find all the new differential geometric and Lie-algebraic methods which are currently used in the theory of integrable systems in this book. It will be indispensable to graduate students and researchers in mathematics and theoretical physics.</p>

Dynamical Systems VII: Integrable Systems Nonholonomic Dynamical Systems (ENCYCLOPAEDIA OF MATHEMATICAL SCIENCES)

Science & Math

A.T.Fomenko

Vladimir I. Arnold

A.M. Perelomov

V. Ya. Gershkovich

M.A. Olshanetsky

Mathematics

Springer, Verlag

<p>The book covers general topology, nonlinear co-ordinate systems, theory of smooth manifolds, theory of curves and surfaces, transformation groups,tensor analysis and Riemannian geometry, theory of integration and homologies, fundamental groups and variational principles in Riemannian geometry. The text is intended for graduate and research students in mathematics and physics. The text is presented in a form that is easily accessible to students and is supplemented by a large number of examples, problems, drawings and appendices.</p>

A Short Course in Differential Geometry and Topology

A.S.Mishchenko

Cambridge Scientific Publishers Ltd

This volume is a companion volume to A Short Course in Differential Geometry and Topology and is based on seminars held at Faculty of Mechanics and Mathematics at Moscow State University. It is intended as a supplementary text for graduate courses in differential geometry and topology. Parts 1 and 2 consist of problems and there are answers and solutions given.

Selected Problems in Differential Geometry and Topology

Y.P.Solovyev

Modern geometry--methods and applications (Graduate texts in mathematics)

Reference

S. P. Novikov

B.A. Dubrovin

Foreign Language Study & Reference

Modern Geometry - Methods and Applications: Part 3: Introduction to Homology Theory

Springer

Variational Principles of Topology: Multidimensional Minimal Surface Theory (Mathematics and its Applications, Volume 42) [Special Indian Edition - Reprint Year: 2020]

SPRINGER NATURE (SIE)

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