Dynamical systems.

Format:

Book

Contributor:

Arnolʹd, V. I. (Vladimir Igorevich), 1937-2010.

Series:

Encyclopaedia of mathematical sciences ; v.1, etc.

Encyclopaedia of mathematical sciences ; v.1-6, 16, 39, 66-67

Standardized Title:

Dinamicheskie sistemy. English

Language:

English

Russian

Subjects (All):

Mechanics, Analytic.

Celestial mechanics.

Physical Description:

volumes : illustrations ; 24 cm.

Place of Publication:

Berlin ; New York : Springer-Verlag, c1988-

Summary:

This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas that appeared in Hamiltonian mechanics, optics and hydrodynamics under different names. In addition, some interesting applications of the general theory of vortices are discussed in the book such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics. The investigation of families of trajectories of Hamiltonian systems can be reduced to problems of multidimensional ideal fluid dynamics. For example, the well-known Hamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested in mathematical physics, mechanics, and the theory of differential equations.

Contents:

1. Ordinary differential equations and smooth dynamical systems / D.V. Anosov, V.I. Arnol'd (eds.)

2. Ergodic theory with applications to dynamical systems and statistical mechanics / Ya.G. Sinai (ed.)

3. Mathematical aspects of classical and celestical mechanics / V. Arnol'd (ed.)

4. Symplectic geometry and its applications / V.I. Arnol'd, S.P. Novikov (eds.)

5. Bifurcation theory and catastrophe theory / V.I. Arnol'd (ed.)

6. Singularity theory I / V.I. Arnol'd (ed.)

7. Integrable systems. Nonholonomic dynamical systems / V.I. Arnol'd, S.P. Novikov (ed.)

8. Singularity theory II. Applications / V.I. Arnol'd (ed.)

9. Dynamical systems with hyperbolic behavior / D.V. Anosov (ed.)

10. General theory of Vortices / V.V. Kozlov.

Notes:

Translation of: Dinamicheskie sistemy, issued as part of the series: Itogi nauki i tekhniki. Serii͡a Sovremennye problemy matematiki.

Includes bibliographical references and index.

ISBN:

0387170022

3540422072

OCLC:

16404140