(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
Leading mathematician and expert teacher, V.I. Arnold turns 60 in June of 1997. This volume contains a selection of original papers prepared for the occasion of this 60th anniversary by former students and other participants in Arnold's Moscow seminar. A weekly event since the mid-1960s, this seminar and its participants have been inspired by Arnold's creative ideas and universal approach to mathematics.
The papers in this volume reflect Arnold's wide range of interests and his scientific contributions, including singularity theory, symplectic and contact geometry, mathematical physics, and dynamical systems. The spirit of this work is consistent with Arnold's view of mathematics, connecting different areas of mathematics and theoretical physics. The book is rich in applications and geometrical in nature.
American Mathematical Society Translations - Series 2,,
Advances in the Mathematical Sciences, Volume 180
July 1997, 255 pages, Hardcover,
ISBN 0-8218-0807-9.
This book presents a unified treatment of output regulation theory for linear and nonlinear systems and addresses a number of issues which were left open in the earlier works on the subject. It describes an approach to structurally stable regulations which unifies and extends a number of prior existing results. It also addresses the issue of robust regulation, i.e. the issue of achieving regulation in the presence of parameter uncertainties ranging within a prescribed set.
1997, 136pp,This book is divided into two parts, with a generic introduction to the concepts of attractor in dynamics preceding description of new results on two research problems. The first part is gentle but rigorous; several different notions of attractor are defined and compared, and the finer points are thoroughly illustrated by examples and counterexamples.
The second part deals with two different problems in discrete dynamics. The first problem is the characterisation of the dynamics on stable w-limit sets with infinitely many components and the second is the study of transverse stability of attractors on an invariant submanifold.
Contents: Attractors in Dynamical Systems, Liapunov Stability and Adding Machines, From Attractor to Chaotic Saddle: a journey through transverse instability.
1997 approx. 148pp,
ISBN 3-7643-5793-2.
The book is an introduction to the theory of nonlinear hyperbolic differential equations. Four chapters are devoted to weak solutions of systems of conservative laws. Two chapters cover the existence of global solutions or estimates of the life-span for solutions of nonlinear perturbations of the ways or Klien-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with the theory of pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of operators needed in the nonlinear theory is presented in complete theory.
1997, app 304pp, ISBN 3-540-62921-1.
Mathematics and Applications, Volume 26.