This book provides readers with a comprehensive survey of models of dynamic games in economics, including an extensive coverage of numerous fields of applications. It will also discuss and explain main concepts and techniques used in dynamic games, and inform readers of its major developments while equipping them with tools and ideas that will aid in the formulation of solutions for problems. A Survey of Dynamic Games in Economics will interest those who wish to study more about the conceptions, approaches and models that are applied in the domain of dynamic games.

... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.

Driven by the increasingly expanding needs of infrastructure construction, operation and maintenance, as well as the rapid developments of intelligent sensing and information technology, precise engineering surveying has been transformed from static, discrete, and manual into dynamic, continuous, and intelligent ways. This transformation leads to an advanced multidisciplinary field, dynamic and precise engineering surveying, on which the author has worked for over two decades. This book systematically summarizes the fundamentals, methods, and applications in dynamic and precise engineering surveying. The contents mainly include two parts: the first part introduces principles and methods of dynamic and precise engineering surveying; the second part presents representative applications in which innovative methods and advanced equipment are applied in the construction, operation and maintenance of mega and complex infrastructures. Readers engaged in surveying and mapping, civil engineering, water conservancy engineering, railway engineering, electronic information, and computer science, including undergraduates, graduates, researchers and engineers, will find it an informative reference.

Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

The conference "Analysis of Controlled Dynamical Systems" was held in July 1990 at the University of LYON FRANCE. About hundred participants attended this conference which lasted four days : There were 50 speakers from departments of Engineering and Mathematics in east and west Europe, USA and USSR. The general subject of the conference was system theory. The main topics were optimal control, structure and control of nonlinear systems, stabilization and observers, differential algebra and systems theory, nonlinear aspects of Hoc theory, rigid and flexible mechanical systems, nonlinear analysis of signals. We are indebted to the scientific committee John BAILLIEUL, Michel FLIESS, Bronislaw JAKUBCZYCK, Hector SUSSMANN, Jan WILLEMS. We gratefully acknowledge the time and thought they gave to this task. We would also like to thank Chris BYRNES for arranging for the publication of these proceedings through the series "Progress in Systems and Control Theory"; BIRKHAUSER. Finally, we are very grateful to the following institutions who through their financial support contributed essentially to the success of this conference : CNRS, Special year " Systemes Dynamiques", DRET, MEN-DAGIC, GRECO-AUTOMATIQUE, Claude Bernard Lyon I University, Entreprise Rhone-Alpes International, Conseil General du RhOne, the cities of LYON and VILLEURBANNE.

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.