Preface

Chapter 7 117

Global Indeterminacy and Invariant Manifolds Near Homoclinic

Orbit to a Real Saddle by Beatrice Venturi

II

It is not exaggerating to state that the subject of chaos has reached nearly every branch of the natural sciences. It has become common to talk about chaotic weather patterns, chaotic evolution in population dynamics, and chaos in atomic physics and chemical reactions. The latter is perhaps a bit surprising at first, since at the atomic level, physics seems governed by the linear laws of quantum mechanics, while an essential ingredient of chaos is nonlinearity in the dynamical equations.

The current volume presents seven very good contributions to this area of research. One of the main contributions of the book is to illustrate the diversity of subjects that have been influenced by this area of research. Of these seven chapters, there are four that examine the issue of chaos in nonlinear and dynamical systems. These look at chaos as it manifests itself in various types of differential equations and systems of differential equations as well as its impact on mathematics in general. There is also a chapter that briefly discusses chaos in quantum mechanics. This will continue to be an important area of research in the future, as experimental techniques have advanced to a level that can be investigated at the atomic and molecular levels. The final two chapters track the progress of chaos into such diverse areas as biology and economics.

The book has been assembled out of the hard work of an international group of invited authors. It is a pleasure to thank them for their work and scientific contributions. I am grateful to acknowledge with much thanks the assistance provided by Ms. Sara Bacvarova, Author Service Manager, as well as the IntechOpen publishing group for the opportunity to work on this volume.

> Paul Bracken Professor, Department of Mathematics, University of Texas, USA

Section 1

Chaos in Quantum

Mechanics

1

Section 1
