Dieses Buch (es ist aus Vorlesungen und Vortragen entstanden, die die Verfasser an der ETH, Zurich, an der Universitat Texas in Austin und anderswo gehalten haben) mochte eine Einfuhrung in die Mittelwertmethode bei gewohnlichen Differentialgleichungssystemen geben, die auch neueren Ent wicklungen Rechnung tragt. Diese Methode hat sich in Theorie und Anwen dung als so fruchtbar erwiesen, dass es gerechtfertigt erscheint, ihr auch ein Buch in der LAMM-Reihe zu widmen. Es gliedert sich wie folgt: Formale Untersuchungen (erstes und drittes Kapitel), Anwendungen (zweites Kapitel), mathematische Begrundung der Methode (viertes Kapitel). Das Buch besitzt folgende Merkmale, auf die hingewiesen sei: (i) Wir ent wickeln die Mittelwertmethode konsequent auf der Grundlage der Lieschen Reihen und befassen uns ausfuhrlich mit den Implikationen dieses Grundkon zepts. (ii) Wir versuchen, anwendungsnahe Beispiele vorzufuhren, insbe sondere werden auch hoherdimensionale Probleme behandelt. Wann immer moglich leiten wir die zu Grunde liegenden Differentialgleichungen her oder interpretieren sie zumindest. (iii) Obwohl wir uns mit diesem Buch an anwendungsorientierte Mathematiker, Ingenieure und Naturwissenschaftler richten, haben wir es fur richtig gehalten, im theoretischen Teil des Buches auch tieftiegende Resultate herzuleiten. Wir haben uns jedoch um einfache und durchsichtige Beweise bemuht, die wir ausfuhrlich darlegen. Auch in den theoretischen Teilen wird immer wieder die Brucke zu den Anwendungen geschlagen. An Vorkenntnissen setzt das Buch die ublichen Vorlesungen uber Analysis und Lineare Algebra voraus, wie sie in den ersten vier Semestern an Hochschulen geboten werden."

Dynamics Reported reports on recent developments in dynamical systems theory. Dynamical systems theory, of course, originated from ordinary differential equations. Today, dynamical systems theory covers a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems theory has evolved remarkably rapidly in the recent years. A wealth of new phenomena, new ideas and new techniques proved to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications have appeared and still will appear. Dynamics Reported presents carefully written articles on major subjects in dynamical systems and their applications, addressed not only to specialists but also to a broader range of readers. Topics are advanced while detailed exposition of ideas, restriction to typical results, rather than to the most general ones and, last but not least, lucid proofs help to gain an utmost degree of clarity. It is hoped that Dynamics Reported will stimulate exchange of ideas among those working in dynamical systems and moreover will be useful for those entering the field.

Dynamics Reported reports on recent developments in dynamical systems theory. Dynamical systems theory of course originated from ordinary differential equations. Today, dynamical systems theory covers a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems theory has evolved remarkably rapidly in the recent years. A wealth of new phenomena, new ideas and new techniques proved to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications have appeared and still will appear. Dynamics Reported presents carefully written articles on major subjects in dynamical systems and their applications, addressed not only to specialists but also to a broader range of readers. Topics are advanced while detailed exposition of ideas, restriction to typical results, rather than to the most general ones, and last but not least lucid proofs help to gain an utmost degree of clarity. It is hoped that Dynamics Reported will stimulate exchange of ideas among those working in dynamical systems and moreover will be useful for those entering the field.