Abstract
The Hartman-Grobman theorem plays an important role in the study of certain nonlinear dynamical systems which are associated with equivariant vector fields with respect to the action of a compact group Γ. On the other hand, orbit space reduction techniques can be a useful tool in the analysis of equivariant dynamical systems. The idea is to project the vector field on the space which is spanned by a basis of the ring of Γ-invariant polynomials. The orbit space can be realized as a stratified variety in this space, and the restriction to the orbit space of the projected system preserves strata. However, nonlinear terms can lead to linear terms by projection. This raises the natural question: which terms in the linearization are really needed, or, else, is there a well-suited Hartman-Grobman theorem in the orbit space?
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Comptes Rendus de l'Academie des Sciences Series I Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
