Ralph Abraham - Böcker

Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.

Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.

The Web Empowerment Book is the first book devoted entirely to the World Wide Web, a hypertext-linked system which enables Internet users to navigate readily through a maze of Web servers and providers. Although there is a wealth of information available on the Internet, this is the first practical "how-to" book to explain in simple, pragmatic terms how to establish your own connection, to navigate through, and understand the WWW. Users with or without previous knowledge will have access to a book which has put the information and solutions regarding the WWW into a well-written, accessible context. This is accomplished in three basic steps: Step 1: Get an account from an Internet provider and a modem, to use utilities at the Internet providers site, and to download files. Step 2: Add SLIP or PPP to your own machine to use your own TCP/IP utilities: Email, Telnet, gopher, FTP, NewsGroups, UseNet, WAIS, Archie, Finger, etc. Step 3: Add World-Wide Web (WWW) Browser and Displayers for: Hypertext, Images, Sounds, Movies.

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus.

In this book of ""trialogues,"" the late psychedelic visionary and shamanologist Terence McKenna, acclaimed biologist and originator of the morphogenetic fields theory Rupert Sheldrake, and mathematician and chaos theory scientist Ralph Abraham explore the relationships between chaos and creativity and their connection to cosmic consciousness. Their observations call into question our current views of reality, morality, and the nature of life in the universe. The authors challenge the reader to the deepest levels of thought with wide-ranging investigations of the ecology of inner and outer space, the role of chaos in the dynamics of human creation, and the resacralization of the world. Among the provocative questions the authors raise are: Is Armageddon a self-fulfilling prophecy? Are we humans the imaginers or the imagined? Are the eternal laws of nature still evolving? What is the connection between physical light and the light of consciousness? Part ceremony, part old-fashioned intellectual discussion, these trialogues are an invitation to a new understanding of what Jean Houston calls ""the dreamscapes of our everyday waking life."

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me­ chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.

Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semi-cascades (discrete, irreversible, dynamical systems). Flows and semi-cascades are the classical systems iuntroduced by Poincare a centry ago, and are the subject of the extensively illustrated book: "Dynamics: The Geometry of Behavior," Addison-Wesley 1992 authored by Ralph Abraham and Shaw. Semi- cascades, also know as iterated function systems, are a recent innovation, and have been well-studied only in one dimension (the simplest case) since about 1950. The two-dimensional case is the current frontier of research. And from the computer graphcis of the leading researcher come astonishing views of the new landscape, such as the Julia and Mandelbrot sets in the beautiful books by Heinz-Otto Peigen and his co-workers. Now, the new theory of critical curves developed byMira and his students and Toulouse provide a unique opportunity to explain the basic concepts of the theory of chaos and bifurcations for discete dynamical systems in two-dimensions. The materials in the book and on the accompanying disc are not solely developed only with the researcher and professional in mind, but also with consideration for the student. The book is replete with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-color animations that are tied directly into the subject matter of the book, itself. In addition, much of this material has also been class-tested by the authors. The cross-platform CD also contains a software program called ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided which give the reader the option of working directly with the code from which the graphcs in the book were