edited by R Ball & N Akhmediev (Australian National University)

NONLINEAR DYNAMICS: FROM LASERS TO BUTTERFLIES
Selected Lectures from the 15th Canberra International Physics Summer School
Australian National University 21 January - 1 February 2002

World Scientific Lecture Notes in Complex Systems - Vol. 1

This book is an inspirational introduction to modern research directions and scholarship in nonlinear dynamics, as well as a valuable reference for researchers in the field. The scholarly level is aimed at the beginning postgraduate student, with a potential readership drawn from disciplines in mathematics and the physical sciences.
In addition to new pedagogical material, each chapter provides a review of the current state of the area and a discussion on open problems. The contributors include Brian Davies (bifurcations in maps), Nalini Joshi (integrable systems and asymptotics), Alan Newell (wave turbulence and pattern formation), Carl Weiss (spatial solitons), Cathy Holmes (Hamiltonian systems), Tony Roberts (dissipative fluid mechanics), John Brindley (nonlinear dynamics in the oceans) and Mike Lieberman (Fermi acceleration).

Readership: Postgraduate students and researchers in mathematics and the physical sciences.

350pp (approx.) Pub. date: Scheduled Summer 2003
ISBN 981-238-320-4

by S S Chern (Nankai Institute of Mathematics, P R China) & Z Shen (Indiana University Purdue University Indianapolis, USA)

RIEMANN-FINSLER GEOMETRY

Nankai Tracts in Mathematics - Vol. 6

Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics. It has applications in many fields of the natural sciences. Curvature is the central concept in Riemann?Finsler geometry. This invaluable textbook presents detailed discussions on important curvatures such the Cartan torsion, the S-curvature, the Landsberg curvature and the Riemann curvature. It also deals with Finsler metrics with special curvature or geodesic properties, such as projectively flat Finsler metrics, Berwald metrics, Finsler metrics of scalar curvature or isotropic S-curvature, etc. Instructive examples are given in abundance, for further description of some important geometric concepts. The text includes the most recent results, although many of the problems discussed are classical.

Contents:

Finsler Metrics
Structure Equations
Equivalence Problem
Geodesics
Non-Riemannian Curvatures
Riemann Curvature
Finsler Metrics of Scalar Curvature
Randers Metrics of Scalar Curvature
Berwald Metrics
Projectively Flat Finsler Metrics

Readership: Graduate students and researchers in differential geometry.

200pp (approx.) Pub. date: Scheduled Fall 2003
ISBN 981-238-357-3
ISBN 981-238-358-1(pbk)

by Kai Lai Chung (Stanford University, USA) & Jean-Claude Zambrini (University of Lisbon, Portugal)

INTRODUCTION TO RANDOM TIME AND QUANTUM RANDOMNESS

Monographs of the Portuguese Mathematical Society - Vol. 1

This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K L Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown.
In the second essay J-C Zambrini shows why quantum physics is not a regular probabilistic theory, but also why stochastic analysis provides new tools for analyzing further the meaning of Feynman's path integral approach and a number of foundational issues of quantum physics far beyond what is generally considered. The role of the time parameter, in this theory, is critically re-examined and a fresh way to approach the long-standing problem of the quantum time observable is suggested.

Contents:

Introduction to Random Time:
Prologue
Stopping
Martingale Stopped
Random Past and Future
Other Times
From First to Last
Gapless Time
Markov Chain in Continuum Time
The Trouble with Infinite
Introduction to Quantum Randomness:
Classical Prologue
Standard Quantum Mechanics
Probabilities in Standard Quantum Mechanics
Feynman's Approach to Quantum Probabilities
Schrodinger's Euclidean Quantum Mechanics
Beyond Feynman's Approach
Time for a Dialogue

Readership: Graduate students in mathematics and physics.

220pp (approx.) Pub. date: Scheduled Summer 2003
ISBN 981-238-388-3
ISBN 981-238-415-4(pbk

edited by Yiu-Chung Hon (City University of Hong Kong, China), Masahiro Yamamoto (University of Tokyo, Japan), Jin Cheng (Fudan University, China) & June-Yub Lee (Ewha Womans University, Korea)

RECENT DEVELOPMENT IN THEORIES AND NUMERICS
Proceedings of the International Conference on Inverse Problems
Hong Kong, China 9 - 12 January 2002

The first International Conference on Inverse Problems was held at the City University of Hong Kong in January 2002. It addressed the theoretical (mathematics), applied (engineering) and development aspects of inverse problems. It was intended to nurture Asian-American European collaborations in this evolving interdisciplinary area.
The scope of the proceedings is wide, reflecting the current flourishing theoretical and numerical researches on inverse problems.

Contents:

Surveys
Theoretical Aspects
Numerical Methods
Solutions to Applied Inverse Problems
Related Topics

Readership: Academics, researchers and engineers in applied mathematics.

472pp Pub. date: Apr 2003
ISBN 981-238-366-2

by Leonid P Lebedev (National University of Colombia, Colombia & Rostov State University, Russia) & Michael J Cloud (Lawrence Technological University, USA)

TENSOR ANALYSIS

Tensor analysis is an essential tool in any science (e.g. engineering, physics, mathematical biology) that employs a continuum description. This concise text offers a straightforward treatment of the subject suitable for the student or practicing engineer. The final chapter introduces the reader to differential geometry, including the elementary theory of curves and surfaces. A well-organized formula list, provided in an appendix, makes the book a very useful reference. A second appendix contains full hints and solutions for the exercises.

Contents:

Preliminaries
Transformations and Vectors
Tensors
Tensor Fields
Elements of Differential Geometry

Readership: Undergraduates in engineering or physics, and engineers.

250pp (approx.) Pub. date: Scheduled Summer 2003
ISBN 981-238-360-3