Book description
A highly valued resource for those who wish to move from the
introductory and preliminary understandings and the measurement of
chaotic behavior to a more sophisticated and precise understanding of
chaotic systems. The authors provide a deep understanding of the
structure of strange attractors, how they are classified, and how the
information required to identify and classify a strange attractor can be
extracted from experimental data.
In its first edition, the Topology of Chaos has been a valuable resource
for physicist and mathematicians interested in the topological analysis
of dynamical systems. Since its publication in 2002, important
theoretical and experimental advances have put the topological analysis
program on a firmer basis. This second edition includes relevant results
and connects the material to other recent developments. Following
significant improvements will be included:
* A gentler introduction to the topological analysis of chaotic systems
for the non expert which introduces the problems and questions that one
commonly encounters when observing a chaotic dynamics and which are well
addressed by a topological approach: existence of unstable periodic
orbits, bifurcation sequences, multistability etc.
* A new chapter is devoted to bounding tori which are essential for
achieving generality as well as for understanding the influence of
boundary conditions.
* The new edition also reflects the progress which had been made towards
extending topological analysis to higher-dimensional systems by
proposing a new formalism where evolving triangulations replace braids.
* There has also been much progress in the understanding of what is a
good representation of a chaotic system, and therefore a new chapter is
devoted to embeddings.
* The chapter on topological analysis program will be expanded to cover
traditional measures of chaos. This will help to connect those readers
who are familiar with those measures and tests to the more sophisticated
methodologies discussed in detail in this book.
* The addition of the Appendix with both frequently asked and open
questions with answers gathers the most essential points readers should
keep in mind and guides to corresponding sections in the book. This will
be of great help to those who want to selectively dive into the book and
its treatments rather than reading it cover to cover.
What makes this book special is its attempt to classify real physical
systems (e. g. lasers) using topological techniques applied to real date
(e. g. time series). Hence it has become the experimenter?s guidebook to
reliable and sophisticated studies of experimental data for comparison
with candidate relevant theoretical models, inevitable to physicists,
mathematicians, and engineers studying low-dimensional chaotic systems.
ROBERT GILMORE, PhD, is a professor in the Physics Department of
Drexel University, Philadelphia, Pennsylvania.
MARC LEFRANC, PhD, is a researcher at the Centre National de la
Recherche Scientifique in the Laboratoire de Physique des Lasers,
Atomes, Molecules at the Universite des Sciences et Technologies de
Lille, France.
The authors are internationally recognized leaders in the field who have
been developing these techniques for about two decades. As active
members in the community they are knowledgeable about the broader
context of their book's subject.
