Charles Flowers

Instability Rules: The Ten Most Amazing Ideas of Modern Science

ISBN: 0-471-38042-3
Cloth
228 Pages
March 2002

a century of remarkable scientific discovery
"We learned that the continents are forever slipping and sliding around the globe, like clothing on a teenager, and the mountains are forever rising, the oceans widening, the volcanoes stoking their furnaces for the next blast.

"Our bodies are a fever of change as our minds perpetually rewire themselves and our genes make uncountable decisions, renewing or growing or misfiring to produce the runaway cancers that may kill us, initiating the instability of mortal decay. . . .

"Within tiny atomic universes, particles pop in and out of being, impossible as that may be to conceive, while atoms collide and meld, buzzing continually in their electrically charged states.

"This, then, was the truth behind many of the defining discoveries of the twentieth century: existence is constant activity."
?from the Preface

Table of Contents:

Preface: It Moves . . . 
1 Hubble and the Expanding Universe.
2 Einstein and the Wonder of Light.
3 Bohr and the Puzzles of the Quantum World.
4 Wegener and the Dance of the Continents.
5 Big Bang, Big Crunch, and Big Bore.
6 Fermat, Godel, and Fuzzy Math.
7 Mendel, Watson, Crick, and the Human Genome.
8 Hominids, Humans, and the Search for Origins.
9 Turing and the Brain as Computer, and Vice Versa.
10 Freud, the Unconscious, and Other Views.
Acknowledgments.
Photo Credits.
Index.

Robert Gilmore

The Topology of Chaos

ISBN: 0-471-40816-6
Cloth
544 Pages
June 2002

A new approach to understanding nonlinear dynamics and strange attractors
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 Dynamics, The Topology of Chaos responds to the fundamental challenge of chaotic systems by introducing a new analysis method?Topological Analysis?which can be used to extract, from chaotic data, the topological signatures that determine the stretching and squeezing mechanisms which act on flows in phase space and are responsible for generating chaotic data. Beginning with an example of a laser that has been operated under conditions in which it behaved chaotically, the authors convey the methodology of Topological Analysis through detailed chapters on:

Discrete Dynamical Systems: Maps
Continuous Dynamical Systems: Flows
Topological Invariants
Branched Manifolds
The Topological Analysis Program
Fold Mechanisms
Tearing Mechanisms
Unfoldings
Symmetry
Flows in Higher Dimensions
A Program for Dynamical Systems Theory
Suitable at the present time for analyzing "strange attractors" that can be embedded in three-dimensional spaces, this groundbreaking approach offers researchers and practitioners in the discipline a complete and satisfying resolution to the fundamental questions of chaotic systems.

Table of Contents:

Preface.
Acknowledgments.
Acronyms.
1. Introduction.
2. Dscrete Dynamical Systems: Maps.
3. Continuous Dynamical Systems: Flows.
4. Topological Invariants.
5. Branched Manifolds.
6. The Topological Analysis Program.
7. Fold Mechanisms - A2.
8. Tearing Mechanisms - A3.
9. Unfoldings.
10. Symmetry.
11. Flows in Higher Dimensions.
12. A Program for Dynamical Systems Theory.
Appendix A: Determining Templates from Topological Invariants.
References.
Glossary.
Index.

Andrew Ranicki,
Department of Mathematics and Statistics, University of Edinburgh

Algebraic and Geometric Surgery

(Hardback )
0-19-850924-3
Publication date: October 2002
Clarendon Press 400 pages, 69 line, 234mm x 156mm
Series: Oxford Mathematical Monographs

Contains several drawings where geometry is used to illustrate the algebra
Extensively referenced
Contains worked examples
Assumes only a basic knowledge differential and algebraic topology

Description
This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students, who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, cobordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.

Readership: Graduate students and researchers using topology in mathematics and physics.

Contents/contributors
Preface
1 The surgery classification of manifolds
2 Manifolds
3 Homotopy and homology
4 Poincare duality
5 Bundles
6 Cobordism theory
7 Embeddings, immersions and singularities
8 Whitehead torsion
9 Poincare complexes and spherical fibrations
10 Surgery on maps
11 The even-dimensional surgery obstruction
12 The odd-dimensional surgery obstruction
13 The structure set
References
Index

Edited by: S. Elaydi, J. Lopez Fenner, G. Ladas, M. Pinto

New Trands in Difference Equations
Proceedings of the Fifth International Conference on Difference Equations

ISBN: 0-415-28389-2

Pub Date: 28 FEB 2002
Type: Hardback Book
Extent: 320 pages
(Dimensions 246x174 mm)

This series of International Conferences on Difference Equations and Applications has established a tradition within the mathematical community bringing together scientists from many different areas of research to highlight current interests, challenges and unresolved problems. This volume comprises selected papers presented at the Fifth International Conference on Difference Equations which was held at Temuco, Chile and Provides a Valuable source of reference for graduates and researchers.

Full Contributors:
R.M. Abu-Sarris, Birzeit University, Palaestine, L.J.S. Allen, Texas Tech University, USA, B. Aulbach, Universitat Augsburg, Germany, S. Castillo, Universidad del Bio-Bio, Chile, S.S. Cheng, Tsing Hua University, Taiwan, K.A. Cunningham, University of Rhode Island, USA, L.Diaz, Universidad de Oriente, Venezuela, S. Elaydi, Trinity University, Texas, USA, J. Lopez Fenner, Departmento de Matrmaticas y Estadistica, Chile, J. Feuer, St Michael's College, Colchester, USA, A Hoffmann, Technical University of IImenau, Germany, J.A. Kennedy, University of Delaware, Newark, USA, J.C. Kesinger, Texas Tech University, USA, M.R.S. Kulenovic, University of Rhode Island, USA, G. Ladas, University of Rhode Island, USA, A. Loskutov, Moscow State University, Russia, B. Marx, Technical University of IImenau, Germany, R. Medina, Universidad de Los Lagos, Chile, R. Metzger, Technical University of IImenau, Germany, R.Naulin, Universidad de Oriente, Venezuela, M. Pint, Universidad de Chile, Chile, A. Rodkina, University of the West Indies, Jamaica, S. Rybalko, Moscow State University, Russia, S. Siegmund, University of Augsburg, Germany, W.S. Sizer, Minnesota State University of Moorhead, USA, V.P.Sriridonov, Joint Institute for Nuclear Research, Russia, S. Valicenti, Unversity of Rhode Island, USA, M. Vielhaber, Universidad de la Frontera, Chile, John A. Yorke^n, University of Maryland at College Park,USA, S.Zhang, Shanghai Jaiotong University, China