Accession Number : ADA322960
Title : Dynamics, Symmetry and PDEs.
Descriptive Note : Final rept. 15 Feb 94-15 Nov 96,
Corporate Author : HOUSTON UNIV TX
Personal Author(s) : Golubitsky, Martin ; Field, Michael ; Melbourne, Ian
PDF Url : ADA322960
Report Date : 18 MAR 1997
Pagination or Media Count : 6
Abstract : Patterns appear in physical, chemical, and biological systems and are characteristically striking and reproducible. Consequently, scientists and mathematicians have developed theories to explain the origins of these patterns. There are several approaches to the study of pattern; ours is based on symmetry and bifurcation. We have investigated both the theory and application of symmetric dynamical systems and its relation to pattern formation. In this work, pattern is identified with invariance under some of the underlying symmetries. In bounded domains, we have investigated bifurcations to spiral waves. We have also investigated chaotic dynamics where the pattern appears as symmetry on average. In a separate direction, we have considered pattern formation in unbounded domains. Our theoretical investigations have included the bifurcation and meandering of spirals and the Ginzburg-Landau theory of spatially extended systems - with application to spatially aperiodic solutions in spatially extended systems. Finally, part of our effort has been devoted to studying the dynamics present in (ordinary) differential equations with symmetry. For example, we have studied stable ergodicity of chaotic attractors in problems with continuous symmetry, and the existence, stability and bifurcations of robust heteroclinic cycles. Some of these ideas are relevant to intermittent magnetic dynamos in rotating Rayleigh-Benard convection.
Descriptors : *PARTIAL DIFFERENTIAL EQUATIONS, *BIFURCATION(MATHEMATICS), CHAOS, SYMMETRY, PATTERNS, GROUPS(MATHEMATICS).
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE