文档介绍：CY119-FMA&FMB 0521583047 March 17, 2003 15:59 Char Count= 0
A FIRST COURSE IN DYNAMICS
with a Panorama of Recent Developments
The theory of dynamical systems is a major mathematical discipline closely
intertwined with all main areas of mathematics. It has greatly stimulated re-
search in many sciences and given rise to the vast new area variously called
applied dynamics, nonlinear science, or chaos theory. This introduction
for senior undergraduate and beginning graduate students of mathemat-
ics, physics, and bines mathematical rigor with copious
examples of important applications. It covers the central topological and
probabilistic notions in dynamics ranging from Newtonian mechanics to
coding theory. Readers need not be familiar with manifolds or measure
theory; the only prerequisite is a basic undergraduate analysis course.
The authors begin by describing the wide array of scientific and mathe-
matical questions that dynamics can address. They then use a progression
of examples to present the concepts and tools for describing asymptotic
behavior in dynamical systems, gradually increasing the level plex-
ity. In the final chapters the panorama introduces modern developments
and applications of dynamics, discussing logistic maps, hyperbolic dynam-
ics, strange attractors, twist maps, closed geodesics, and applications to
number theory.
Boris Hasselblatt is Professor of Mathematics at Tufts University.
of the Center for Dynamical Systems at The Pennsylvania State University.
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CY119-FMA&FMB 0521583047 March 17, 2003 15:59 Char Count= 0
A FIRST COURSE IN
DYNAMICS
with a Panorama of Recent
Developments
BORIS HASSELBLATT
Tufts University
ANATOLE KATOK
The Pennsylvania State University
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