This is akin to a recipe book written by someone who thinks cooking is impossible, so all he can really write about is grocery shopping. NOT recommended! A much better book is "Trading on the Edge" by Deboeck.
The only cool thing about the book is that you can use it to impress your friends/enemies with the title and loads of arcane equations inside.
the title of the book is mis-leading... it would be as if
a calculus textbook were to call itself "calculus in the markets"
simply because they have a section on compound interest...
2) there is a lot of hand-waving in the theory that is covered.
the author does cover a lot of ground, so it is understandable
that more details and explanations of certain subjects are
not provided. this book *is* a good bibliographic reference,
for example if one is interested in a particular topic, it
could be looked up in this book, and references to all the
seminal works are given.
3) there are better books out there that cover similar subject
matter, and *are* centered on the marketplace: for example,
Mandlebrot's "Fractals and Scaling in Finance", Lo and
MacKinlay's "A Non-Random Walk Down Wallstreet", William Brock
et al "Nonlinear Dynamics, Chaos, and Instability", and
several books by Edgar Peters.
If you are interested in the mathematics of chaos and
dynamical systems, this might be a good book for you.
However, this book is densely packed with mathematics
and unless you have a very solid mathematical background,
Peitgen, Jurgens and Saupe's wonderful book "Chaos and
Fractals: New Frontiers of Science" might be a better choice.
This book covers the basic mathematics of dynamical systems
but does not delve into graduate level mathematics.
If you are thinking of buying this book because its title
mentions markets and non-linear financial time series,
save your money. The author spends five very mathematically
laden chapters discussing dynamical systems. There is nothing
solid on applying the mathematics of dynamical systems to
financial time series other than the observation that they
sure seem chaotic. At the very end the author weakly suggests
that dynamical systems theory might be applied to market
information, but he provides no examples.
People who develop successful market models usually don't
publish much on them, since there is a lot to be gained
by trading them. So one cannot catagorically state what has
and has not been done. However, I know of no case where
dynamical systems mathematics has been used to successfully
provide predictive models (e.g., models you can trade and
make money on) of financial markets. This book certainly does
not live up to the promise of its title.
There are a number of good book on time series analysis and
modeling. For example, see "Wavelet Methods for Time Series Analysis" by Donald B. Percival, Andrew T. Walden. This book
does not deal with financial time series directly, but it does
deal with "non-stationary" time series.