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Full Description
The behaviour under iteration of unimodal maps of an
interval, such as the logistic map, has recently attracted
considerable attention. It is not so widely known that a
substantial theory has by now been built up for arbitrary
continuous maps of an interval. The purpose of the book is
to give a clear account of this subject, with complete
proofs of many strong, general properties. In a number of
cases these have previously been difficult of access. The
analogous theory for maps of a circle is also surveyed.
Although most of the results were unknown thirty years ago,
the book will be intelligible to anyone who has mastered a
first course in real analysis. Thus the book will be of use
not only to students and researchers, but will also provide
mathematicians generally with an understanding of how simple
systems can exhibit chaotic behaviour.
Contents
Periodic orbits.- Turbulence.- Unstable manifolds and homoclinic points.- Topological dynamics.- Topological dynamics (continued).- Chaotic and non-chaotic maps.- Types of periodic orbits.- Topological Entropy.- Maps of the circle.
