Geometrical dynamics of complex systems. A unified modelling approach to physics, control, biomechanics, neurodynamics and psycho-socio-economical dynamics. (English) Zbl 1092.53001
International Series on Microprocessor-Based and Intelligent Systems Engineering 31. Dordrecht: Springer (ISBN 1-4020-4544-1/hbk; 1-4020-4545-X/ebook). xxiii, 822 p. (2006).
As it is mentioned in the preface this is “a graduate-level monographical textbook. It represents a comprehensive introduction into rigorous geometrical dynamics of complex systems of various natures”.
Chapter 1 contains plenty of basic and introductory information on mathematical methods which are used in modern theory of complex systems: smooth manifolds, Lie groups, Riemannian, Finsler, Kähler and symplectic manifolds, fibre bundles, jet spaces, path integrals etc. Chapter 2 in the same manner introduces a variety of complex systems originating from mechanics, physics, control theory, human-like biomechanics, neurodynamics, socio-economic dynamics etc. This book has to be recommended for graduates in applied mathematics who are interested in basics of modern mathematical methods mostly based on geometry.
Chapter 1 contains plenty of basic and introductory information on mathematical methods which are used in modern theory of complex systems: smooth manifolds, Lie groups, Riemannian, Finsler, Kähler and symplectic manifolds, fibre bundles, jet spaces, path integrals etc. Chapter 2 in the same manner introduces a variety of complex systems originating from mechanics, physics, control theory, human-like biomechanics, neurodynamics, socio-economic dynamics etc. This book has to be recommended for graduates in applied mathematics who are interested in basics of modern mathematical methods mostly based on geometry.
Reviewer: Iskander A. Taimanov (Novosibirsk)
MSC:
| 53-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry |
| 58-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis |
| 37-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory |
| 58A20 | Jets in global analysis |
| 34C40 | Ordinary differential equations and systems on manifolds |
| 92-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology |
| 93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
