This volume contains lectures from the Conference Board of Mathematical Sciences meeting held at the University of Colorado on May 31-June 4, 1976. The lectures consist of an expository discussion of basic results for topological flows and a somewhat more detailed discussion of isolated invariant sets and continuation. The construction of the index for isolated invariant sets is new and allows more general application than previous ones. Also, the index itself is endowed with more structure and the continuation theorem is modified to take this new structure into account. Some elementary applications are given, but the main emphasis is on the abstract theory.

ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 1418, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. 166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrvdinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.

This volume contains expository lectures from the Conference Board of the Mathematical Sciences Regional Conference held at Northern Illinois University on July 25-29, 1977.

This volume contains the lecture notes written by the four principal speakers at the C.I.M.E. session on Dynamical Systems held at Montecatini, Italy in June 1994. The goal of the session was to illustrate how methods of dynamical systems can be applied to the study of ordinary and partial differential equations. Topics in random differential equations, singular perturbations, the Conley index theory, and non-linear PDEs were discussed. Readers interested in asymptotic behavior of solutions of ODEs and PDEs and familiar with basic notions of dynamical systems will wish to consult this text.

This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.

This is a progress report on an experimental program, begun a year ago, in the exploration of resonant furcations (= catastrophes) by analog simulation and direct observation - the macroscope program.