(Advances in Applied Mathematics) 2nd Edition
by Robert L. Devaney (Author)
The long-anticipated revision of this well-liked textbook offers many new additions. In
the twenty-five years since the original version of this book was
published, much has happened in dynamical systems. Mandelbrot and Julia
sets were barely ten years old when the first edition appeared, and most
of the research involving these objects then centered around iterations
of quadratic functions. This research has expanded to include all sorts
of different types of functions, including higher-degree polynomials,
rational maps, exponential and trigonometric functions, and many others.
Several new sections in this edition are devoted to these topics.
The area of dynamical systems covered in A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition is
quite accessible to students and also offers a wide variety of
interesting open questions for students at the undergraduate level to
pursue. The only prerequisite for students is a one-year calculus course
(no differential equations required); students will easily be exposed
to many interesting areas of current research. This course can also
serve as a bridge between the low-level, often non-rigorous calculus
courses, and the more demanding higher-level mathematics courses.
Features
- More extensive coverage of fractals, including objects like the Sierpinski carpet and others
that appear as Julia sets in the later sections on complex dynamics, as well as an actual
chaos "game."
- More detailed coverage of complex dynamical systems like the quadratic family
and the exponential maps.
- New sections on other complex dynamical systems like rational maps.
- A number of new and expanded computer experiments for students to perform.
