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The purpose of the conference was to represent recent developments
in measure theoretic, differentiable and topological dynamical
systems as well as connections to probability theory, stochastic
processes, operator theory and statistical physics. Only original
research papers that do not appear elsewhere are included in the
proceedings. Their topics include: C(2)-diffeomorphisms of compact
Riemann manifolds, geodesic flows, chaotic behaviour in billards,
nonlinear ergodic theory, central limit theorems for subadditive
processes, Hausdorff measures for parabolic rational maps, Markov
operators, periods of cycles, Julia sets, ergodic theorems. From
the Contents: L.A. Bunimovich: On absolutely focusing mirrors.- M.
Denker, M. Urbanski: The dichotomy of Hausdorff measures and
equilibrium states for parabolic rational maps.- F. Ledrappier:
Ergodic properties of the stable foliations.- U. Wacker: Invariance
principles and central limit theorems for nonadditive stationary
processes.- J. Schmeling, R. Siegmund-Schultze: Hoelder continuity
of the holonomy map for hyperbolic basic sets.- A.M. Blokh: The
spectral decomposition, periods of cycles and Misiurewicz
conjecture for graph maps.- and contributions by Chr. Bandt and K.
Keller, T. Bogenschutz andH. Crauel, H.G. Bothe, M. Denker and K.F.
Kramer, T.P. Hill and U. Krengel, A. Iwanik, Z.S. Kowalski, E.
Lesigne, J. Malczak, I. Mizera, J. Sipos, R. Wittmann.
The series is devoted to the publication of monographs and
high-level textbooks in mathematics, mathematical methods and their
applications. Apart from covering important areas of current
interest, a major aim is to make topics of an interdisciplinary
nature accessible to the non-specialist. The works in this series
are addressed to advanced students and researchers in mathematics
and theoretical physics. In addition, it can serve as a guide for
lectures and seminars on a graduate level. The series de Gruyter
Studies in Mathematics was founded ca. 35 years ago by the late
Professor Heinz Bauer and Professor Peter Gabriel with the aim to
establish a series of monographs and textbooks of high standard,
written by scholars with an international reputation presenting
current fields of research in pure and applied mathematics. While
the editorial board of the Studies has changed with the years, the
aspirations of the Studies are unchanged. In times of rapid growth
of mathematical knowledge carefully written monographs and
textbooks written by experts are needed more than ever, not least
to pave the way for the next generation of mathematicians. In this
sense the editorial board and the publisher of the Studies are
devoted to continue the Studies as a service to the mathematical
community. Please submit any book proposals to Niels Jacob.
The fifth volume of Rudolf Ahlswede's lectures on Information
Theory focuses on several problems that were at the heart of a lot
of his research. One of the highlights of the entire lecture note
series is surely Part I of this volume on arbitrarily varying
channels (AVC), a subject in which Ahlswede was probably the
world's leading expert. Appended to Part I is a survey by Holger
Boche and Ahmed Mansour on recent results concerning AVC and
arbitrarily varying wiretap channels (AVWC). After a short Part II
on continuous data compression, Part III, the longest part of the
book, is devoted to distributed information. This Part includes
discussions on a variety of related topics; among them let us
emphasize two which are famously associated with Ahlswede:
"multiple descriptions", on which he produced some of the best
research worldwide, and "network coding", which had Ahlswede among
the authors of its pioneering paper. The final Part IV on
"Statistical Inference under Communication constraints" is mainly
based on Ahlswede's joint paper with Imre Csiszar, which received
the Best Paper Award of the IEEE Information Theory Society. The
lectures presented in this work, which consists of 10 volumes, are
suitable for graduate students in Mathematics, and also for those
working in Theoretical Computer Science, Physics, and Electrical
Engineering with a background in basic Mathematics. The lectures
can be used either as the basis for courses or to supplement them
in many ways. Ph.D. students will also find research problems,
often with conjectures, that offer potential subjects for a thesis.
More advanced researchers may find questions which form the basis
of entire research programs.
Stochastik ist die Mathematik des Zufalls. Sie ist von grosster
Bedeutung fur die Berufspraxis der Mathematiker. An vielen Schulen
hat sie ihren festen Platz gefunden. Die beiden Hauptgebiete der
Stochastik sind Wahrscheinlichkeitstheorie und Statistik.
in die Wahrscheinlichkeitstheorie und Statistik Friedr. Vieweg
& Sohn Braunschweig I Wiesbaden Der Verlag Vieweg ist ein
Unternehmen der Verlagsgruppe Bertelsmann. Alle Rechte vorbehalten
(c) Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
1988 Das Werk einschliesslich aller seiner Teile ist
urheberrechtlich geschutzt. Jede Verwertung ausserhalb der engen
Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlags
unzulassig und stratbar. Das gilt insbesondere fur
Vervielfaltigungen, UEbersetzungen, Mikroverfilmungen und die
Einspeicherung und Verarbeitung in elektronischen Systemen. Satz:
Vieweg, Braunschweig Buchbinderische Verarbeitung: W.
Langeluddecke, Braunschweig ISBN 978-3-528-07259-9 ISBN
978-3-322-96418-2 (eBook) DOI 10.1007/978-3-322-96418-2 v Vorwort
Dieses Buch entstand aus einem Skript fur eine in Goettingen
regelmassig gehaltene vierstUEI1dige einfuhrende Vorlesung fur
Mathematiker, Physiker und Lehramtskandidaten. Da das Skript auch
an vielen anderen Universitaten Freunde gefunden hat, habe ich mich
zur Publikation entschlossen. Stochastik ist die Mathematik des
Zufalls. Sie ist von groesster Bedeutung fur die Berufspraxis der
Mathematiker. An vielen Schulen hat sie ihren festen Platz
gefunden. Die beiden Hauptgebiete der Stochastik sind
Wahrscheinlichkeitstheorie und Statistik. In der
Wahrscheinlichkeitstheorie untersucht man zufallige Prozesse mit
festen als bekannt angenommenen steuernden Wahrscheinlichkeiten.
Dies ist theoretisch und praktisch von eigenstandigem Interesse.
Daruber hinaus liefert die Wahrscheinlichkeits- theorie Grundlagen
fur die Statistik, in der aus beobachteten Daten Schlusse uber
unbe- kannte Wahrscheinlichkeiten und uber zweckmassiges Verhalten
gezogen werden sollen.
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