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On symmetric attractors in reversible dynamical systems
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UNSPECIFIED (1998) On symmetric attractors in reversible dynamical systems. In: Workshop on TimeReversal Symmetry in Dynamical Systems, WARWICK, ENGLAND, DEC 0923, 1996. Published in: PHYSICA D, 112 (12). pp. 281297.
Full text not available from this repository.Abstract
Let Gamma subset of O(n) be a finite group acting orthogonally on R ". We say that Gamma is a reversing symmetry group of a homeomorphism, diffeomorphism or flow f(t) : R " (bar right arrow) R " (t epsilon Z or t epsilon R) if Gamma has an index two subgroup <(Gamma)over bar> whose elements commute with f(t) and for all elements rho epsilon Gamma  <(Gamma)over bar> and all t, f(t) circle rho(x) = rho circle f(t)(x). We give necessary group and representation theoretic conditions for subgroups of reversing symmetry groups to occur as symmetry groups of attractors (Lyapunov stable omegalimit sets). These conditions arise due to topological obstructions.
In dimensions 1 and 2 we present a complete description of possible symmetry groups of asymptotically stable attractors for homeomorphisms and diffeomorphisms (these attractors cannot possess reversing symmetries). We also have a fairly complete description in the context of subgroups which contain reversing symmetries. For ail dimensions n we present complete results on the possible symmetry groups of connected asymptotically stable attractors.
In addition, we summarize our results in the context of reversible equivariant flows, which are complete in dimensions 1 and 2 as well as for subgroups of <(Gamma)over bar> subset of O(n) in any dimension n. A survey of the corresponding results in the equivariant context is also given.
Item Type:  Conference Item (UNSPECIFIED)  

Subjects:  Q Science > QA Mathematics Q Science > QC Physics 

Journal or Publication Title:  PHYSICA D  
Publisher:  ELSEVIER SCIENCE BV  
ISSN:  01672789  
Official Date:  15 January 1998  
Dates: 


Volume:  112  
Number:  12  
Number of Pages:  17  
Page Range:  pp. 281297  
Publication Status:  Published  
Title of Event:  Workshop on TimeReversal Symmetry in Dynamical Systems  
Location of Event:  WARWICK, ENGLAND  
Date(s) of Event:  DEC 0923, 1996  
URI:  http://wrap.warwick.ac.uk/id/eprint/16061 
Data sourced from Thomson Reuters' Web of Knowledge
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