Iteration Theory and its Functional Equations Proceedings of the Int

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1163 Iteration Theory and its Functional Equations Proceedings of the International Symposium held at Schloss Hofen (Lochau), Austria Sept. 28-0ct. 1, 1984

Edited by R. Liedl, L. Reich and Gy. Targonski

Springer-Verlag Berlin Heidelberg

Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann

1163 Iteration Theory and its Functional Equations Proceedings of the International Symposium held at Schloss Hofen (Lochau), Austria Sept. 28-0ct. 1, 1984

Edited by R. Liedl, L. Reich and Gy. Targonski

Springer-Verlag Berlin Heidelberg

Editors

Roman Liedl Institut fUr Mathematik, Universitat Innsbruck Innrain 52, 6020 Innsbruck, Austria Ludwig Reich Institut fur Mathematik, Universitat Graz Brandhofgasse 18,8010 Graz, Austria Gyorgy Targonski Fachbereich Mathematik, Universitat Marburg, Lahnberge 3550 Marburg, Federal Republic of Germany

Mathematics Subject Classification (1980): 39-xx, 58Fxx, 70Kxx, 92-xx ISBN 3-540-16067-1 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-16067-1 Springer-Verlag New York Heidelberg Berlin Tokyo

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© by Springer-Verlag Berlin Heidelberg 1985 Printed in Germany Printing and binding; Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210

INTRODUCTION These are the Proceedings of the International Symposium on Iteration Theory and its Functional Equations held at Schloss Hofen in Lochau, (Vorarlberg, Austria), Sept. 28 to Oct. 1, 1984. It was the fifth in a series of international meetings on iteration theory, following Toulouse (1973), Schloss Retzhof near Graz (1977), Amoneburg near Marburg (1980) and again Toulouse (1982). We hope there will be further meetings. Many of the papers are of the convential "definition­theorem­proof" type of mathematics. Several others could be thought of as belonging to "experimental mathematics". The term is a controversial one and we do not wish to imply that all, or even that some,of the authors in question would classify their work under experimental mathematics. We personally feel there is nothing wrong with this term. Used by P.R. Stein and S. Ulam as early as 1964 it means numerical work, usually with a graphic display of the results, and formulating conjectures based on these numerical and graphic results, often also furnishing a rigorous mathematical proof. One paper (Rossler's) ventures into "no man's land" between mathematics. physics and philosophy, offering stimulating heuristic ideas. The overall impact of the symposium was summed up in a "round­table discussion" held on the evening of the last day. The fundamental question, of course, was "What is iteration theory?" and it was answered implicitly