This book discusses many of the common scaling properties observed in
some nonlinear dynamical systems mostly described by mappings. The
unpredictability of the time evolution of two nearby initial conditions
in the phase space together with the exponential divergence from each
other as time goes by lead to the concept of chaos. Some of the
observables in nonlinear systems exhibit characteristics of scaling
invariance being then described via scaling laws.
From the variation of control parameters, physical observables in the
phase space may be characterized by using power laws that many times
yield into universal behavior. The application of such a formalism has
been well accepted in the scientific community of nonlinear dynamics.
Therefore I had in mind when writing this book was to bring together few
of the research results in nonlinear systems using scaling formalism
that could treated either in under-graduation as well as in the post
graduation in the several exact programs but no earlier requirements
were needed from the students unless the basic physics and mathematics.
At the same time, the book must be original enough to contribute to the
existing literature but with no excessive superposition of the topics
already dealt with in other text books. The majority of the Chapters
present a list of exercises. Some of them are analytic and others are
numeric with few presenting some degree of computational complexity.
