San Antonio College Library

"This textbook is a basic introduction to chaos. It is written primarily for advanced undergraduate students in science but postgraduate students and researchers in mathematics, physics and other areas of science will also find the book useful. The authors concentrate on explaining the fundamentals of the subject by studying examples from one-dimensional maps and simple differential equations."--Jacket.

"This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. The theory is developed using only elementary calculus and algebra, and includes dynamics of one- and two-dimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and bifurcation theory of one-dimensional systems. Here is an introduction to the theory...

Does God Play Dice? explains the astonishing new theories of systems that obey simple laws but which are neither constant nor predictable. Ian Stewart reveals a strange universe, one in which nothing may be as it seems, where familiar geometrical shapes such as circles and ellipses give way to infinitely complex structures known as 'fractals.' He explains how the fluttering of a butterfly's wing can change the weather and how the gravitational attraction...

The author describes how scientists studying the growth of complexity in nature are discovering order and pattern in chaos. He explains concepts such as nonlinearity, the Butterfly Effect, universal constants, fractals, and strange attractors, and examines the work of scientists such as Mitchell J. Feigenbaum, Edward Lorenz, and Benoit Mandelbrot.

Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincare submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincare found a serious mistake...

"What do traffic jams, stock market crashes, and wars have in common? They are all explained using complexity, an unsolved puzzle that many researchers believe is the key to predicting - and ultimately solving - everything from terrorist attacks and pandemic viruses right down to rush hour traffic congestion." "In Two's Company, Three is Complexity, international expert Neil Johnson provides a readable account of this fledgling field of science. Arming...

Why does time seem to fly on some occasions and drag on others? Why do some societies seem more prone to totalitarianism than others? Why does atonal music sound "worse" to most of us than traditional music? How can a butterfly in Brazil affect the weather in Alaska? The set of ingenious interdisciplinary approaches that are, together, called the science of complexity offers answers to these and dozens of other questions that beg the larger question...

"The behavior of a physical system may appear irregular or chaotic even when it is completely deterministic and predictable for short periods of time into the future. How does one model the dynamics of a system operating in a chaotic regime? Older tools such as estimates of the spectrum of Lyapunov exponents and estimates of the spectrum of fractal dimensions do not sufficiently answer this question. In a significant evolution of the field of Nonlinear...