Symplectic geometry of integrable Hamiltonian systems

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Tudor Ratiu

The papers in this volume are an outgrowth of some of the lectures and informal discussions that took place during the workshop on the geometry of Hamiltonian systems, held at the MSRI in Berkeley in June of 1989. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, numerical simulations and dynamical systems in general. The articles are of differing lengths and scopes; some are research announcements while others are surveys of particularly active areas of interest where the results can only be found in scattered research articles and preprints. In- cluded in the book is A.T. Fomenko's survey of the classification of integrable systems.

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V.I. Elkin

This monograph is devoted to methods of reduction of nonlinear control systems to a simpler form: for example, decomposition into systems of lesser dimension. The approach centres on the immersion of control systems into some differential geometric category. Within the framework of this category the reduction of control systems becomes a reduction to isomorphic objects, quotient objects, and subobjects. The theory of reduction of nonlinear control systems discussed here outlines the elements of the general theory of such systems, which is of necessity purely differential geometric by nature. Audience: This book will be of interest to graduate students as well as to researchers who wish to gain insight into the modern differential geometric theory of nonlinear control systems.

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Lorna Holtman ... [et al

Much attention in late-developing countries is given to providing access to studies which allow school leavers to enter science and technology-related careers. These programmes are driven by the belief that graduates will then substantially contribute to the developmental needs of their countries. But is providing access to institutions enough? Students in developing countries often come from school environments lacking in resources - human, physical and financial. This book, in a number of chapters, reviews research related to the crucial dimension of epistemological access to the disciplines of import, which students need as much as institutional access in order to improve their chances of success. A significant feature of this collection's research studies is that their empirical bases are highly localised, covering areas such as: research methods; access; curriculum, instruction and assessment; and the relevance of science and mathematics education in Zimbabwe, Uganda, Swaziland, South Africa, Namibia, Malawi, Ghana and Lesotho. This volume provides invaluable insights and will be of relevance to researchers, policy makers and lecturers interested in these research outcomes in Sub-Saharan Africa. It is the outcome of a doctoral research capacity-development project, the Graduate Studies in Science, Mathematics and Technology Education (GRASSMATE).

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A. Halanay, V. Răsvan

This volume, which coincides with the centennial anniversary of the publication of the celebrated monograph The General Problem of the Stability Motion by A.M. Liapunov, reviews the current state of the art of the theory and applications of the Liapunov methods. The book contains an Introduction and four chapters. Chapter 2 presents some general results in stability theory. The remaining chapters deal with applications in power engineering, chemical engineering, and in non-engineering fields such as economics and in the modelling of interacting species. The beauty of the results obtained, the diversity of mathematical tools employed, and the described approach to mathematical modelling provide stimulating considerations for applications in many other fields. For mathematicians and engineers whose work involves the study and applications of stability theory in systems.