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Complex Dynamics: Families and Friends features contributions by
many of the leading mathematicians in the field, such as Mikhail
Lyubich, John Milnor, Mitsuhiro Shishikura, and William Thurston.
Some of the chapters, including an introduction by Thurston to the
general subject of complex dynamics, are classic manuscripts that
were never published before but have influenced the field for more
than two decades. Other chapters contain fresh, original work and
bring readers to the current frontier of research. The title
reflects the fruitful interplay between diverse mathematical fields
bound together by the common theme of complex dynamics, including
hyperbolic geometry, number theory, group theory, combinatorics,
general dynamics, and many more. At the same time, the title
alludes to the spirit of mathematical friendship among the
researchers in this area. This book is a tribute to John Hubbard,
one of the most inspiring pioneers in the field of complex
dynamics.
Complex Dynamics: Families and Friends features contributions by
many of the leading mathematicians in the field, such as Mikhail
Lyubich, John Milnor, Mitsuhiro Shishikura, and William Thurston.
Some of the chapters, including an introduction by Thurston to the
general subject of complex dynamics, are classic manuscripts that
were never published before but have influenced the field for more
than two decades. Other chapters contain fresh, original work and
bring readers to the current frontier of research. The title
reflects the fruitful interplay between diverse mathematical fields
bound together by the common theme of complex dynamics, including
hyperbolic geometry, number theory, group theory, combinatorics,
general dynamics, and many more. At the same time, the title
alludes to the spirit of mathematical friendship among the
researchers in this area. This book is a tribute to John Hubbard,
one of the most inspiring pioneers in the field of complex
dynamics.
In July 2009 Germany hosted the 50th International Mathematical
Olympiad (IMO). For the very first time the number of participating
countries exceeded 100, with 104 countries from all continents.
Celebrating the 50th anniversary of the IMO provides an ideal
opportunity to look back over the past five decades and to review
its development to become a worldwide event. This book is a report
about the 50th IMO as well as the IMO history. A lot of data about
all the 50 IMOs are included. We list the most successful
contestants, the results of the 50 Olympiads and the 112 countries
that have ever taken part. It is impressive to see that many of the
world's leading research mathematicians were among the most
successful IMO participants in their youth. Six of them gave
presentations at a special celebration: Bollobas, Gowers, Lovasz,
Smirnov, Tao and Yoccoz. This book is aimed at students in the IMO
age group and all those who have interest in this worldwide leading
competition for highschool students.
The theory of holomorphic dynamical systems is a subject of
increasing interest in mathematics, both for its challenging
problems and for its connections with other branches of pure and
applied mathematics. A holomorphic dynamical system is the datum of
a complex variety and a holomorphic object (such as a self-map or a
vector ?eld) acting on it. The study of a holomorphic dynamical
system consists in describing the asymptotic behavior of the
system, associating it with some invariant objects (easy to
compute) which describe the dynamics and classify the possible
holomorphic dynamical systems supported by a given manifold. The
behavior of a holomorphic dynamical system is pretty much related
to the geometry of the ambient manifold (for instance, - perbolic
manifolds do no admit chaotic behavior, while projective manifolds
have a variety of different chaotic pictures). The techniques used
to tackle such pr- lems are of variouskinds: complexanalysis,
methodsof real analysis, pluripotential theory, algebraic geometry,
differential geometry, topology. To cover all the possible points
of view of the subject in a unique occasion has become almost
impossible, and the CIME session in Cetraro on Holomorphic
Dynamical Systems was not an exception.
This Invitation to Mathematics consists of 14 contributions, many
from the world's leading mathematicians, which introduce the
readers to exciting aspects of current mathematical research. The
contributions are as varied as the personalities of active
mathematicians, but together they show mathematics as a rich and
lively field of research. The contributions are written for
interested students at the age of transition between high school
and university who know high school mathematics and perhaps
competition mathematics and who want to find out what current
research mathematics is about. We hope that it will also be of
interest to teachers or more advanced mathematicians who would like
to learn about exciting aspects of mathematics outside of their own
work or specialization. Together with a team of young ``test
readers'', editors and authors have taken great care, through a
substantial ``active editing'' process, to make the contributions
understandable by the intended readership.
Diese Einladung zur Mathematik besteht aus 14 Beitragen, viele
davon von weltweit fuhrenden Mathematikern geschrieben, die die
Leser in spannende Aspekte aktueller mathematischer Forschung
einfuhren. Die Artikel sind so vielfaltig wie die Persoenlichkeiten
ihrer Autoren und zeigen, wie reich und lebendig die Mathematik als
Forschungsgebiet ist. Das Buch richtet sich in erster Linie an
interessierte Schuler und junge Studierende, die Mathematik aus der
Schule oder von Wettbewerben kennen und die aktuelle
Forschungsmathematik kennenlernen wollen. Zusammen mit einem Team
junger Testleser haben die Herausgeber und Autoren in einem
intensiven Bearbeitungsprozess die Texte fur junge Leser
verstandlich gestaltet. Schuler, Lehrer, Mathematiker und alle
Mathematik-Begeisterten werden in diesem vielseitigen und
spannenden Buch genussvoll lesen.
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