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This third edition text provides expanded material on the
restricted three body problem and celestial mechanics. With each
chapter containing new content, readers are provided with new
material on reduction, orbifolds, and the regularization of the
Kepler problem, all of which are provided with applications. The
previous editions grew out of graduate level courses in
mathematics, engineering, and physics given at several different
universities. The courses took students who had some background in
differential equations and lead them through a systematic grounding
in the theory of Hamiltonian mechanics from a dynamical systems
point of view. This text provides a mathematical structure of
celestial mechanics ideal for beginners, and will be useful to
graduate students and researchers alike. Reviews of the second
edition: "The primary subject here is the basic theory of
Hamiltonian differential equations studied from the perspective of
differential dynamical systems. The N-body problem is used as the
primary example of a Hamiltonian system, a touchstone for the
theory as the authors develop it. This book is intended to support
a first course at the graduate level for mathematics and
engineering students. ... It is a well-organized and accessible
introduction to the subject ... . This is an attractive book ... ."
(William J. Satzer, The Mathematical Association of America, March,
2009) "The second edition of this text infuses new mathematical
substance and relevance into an already modern classic ... and is
sure to excite future generations of readers. ... This outstanding
book can be used not only as an introductory course at the graduate
level in mathematics, but also as course material for engineering
graduate students. ... it is an elegant and invaluable reference
for mathematicians and scientists with an interest in classical and
celestial mechanics, astrodynamics, physics, biology, and related
fields." (Marian Gidea, Mathematical Reviews, Issue 2010 d)
This IMA Volume in Mathematics and its Applications TWIST MAPPINGS
AND THEIR APPLICATIONS is based on the proceedings of a workshop
which was an integral part of the 1989- 90 IMA program on
"Dynamical Systems and their Applications". The workshop brought
together many of the leading figures in the modern study of twist
maps. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee,
Ken Meyer, Jiirgen Moser, Clark Robinson, George R. Sell, and
Eduard Zehnder for organizing the meeting and, especially, Richard
McGehee and Ken Meyer for editing the volume. A vner Friedman
Willard Miller, Jr. PREFACE In the 1890 volume of Acta Mathematica,
H. Poincare published his prize- winning paper on the stability of
orbits of the three body problem. In that paper, he introduced some
of the basic ideas about twist maps of the annulus. One hun- dred
years later, the study of twist maps is still an active and
important area of dynamical systems theory.
This IMA Volume in Mathematics and its Applications COMPUTER AIDED
PROOFS IN ANALYSIS is based on the proceedings of an IMA
Participating Institutions (PI) Conference held at the University
of Cincinnati in April 1989. Each year the 19 Participating
Institutions select, through a competitive process, several
conferences proposals from the PIs, for partial funding. This
conference brought together leading figures in a number of fields
who were interested in finding exact answers to problems in
analysis through computer methods. We thank Kenneth Meyer and
Dieter Schmidt for organizing the meeting and editing the
proceedings. A vner Friedman Willard Miller, Jr. PREFACE Since the
dawn of the computer revolution the vast majority of scientific
compu tation has dealt with finding approximate solutions of
equations. However, during this time there has been a small cadre
seeking precise solutions of equations and rigorous proofs of
mathematical results. For example, number theory and combina torics
have a long history of computer-assisted proofs; such methods are
now well established in these fields. In analysis the use of
computers to obtain exact results has been fragmented into several
schools."
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