From: pecora@zoltar.nrl.navy.mil (Lou Pecora) Subject: Re: symmetries groups and dynamical systems Date: 4 Dec 1999 11:30:02 -0600 Newsgroups: sci.math.research In article <944180727.175717096@news.fnac.net>, Romain Brette wrote: > I'm looking for a good introduction about symmetries groups for dynamical > systems. In particular, I consider equations like > dx/dt=f(x) > where x is a finite-dimensional vector, and I'm interested in two types of > symmetries: > symmetries of the vector field : f(sx)=f(x) > symmetries that transform a solution into another solution: if x is solution, > sx is also a solution > > For instance, I'm interested in permutation groups (if you permute the > variables, the system is unchanged). What does it tell you about the behaviour > of the solutions ? > Thank you Not all of these are introductory, but check out, [1] M. Golubisky, I.N. Stewart, and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, vol. II (Springer-Verlag, Berlin, 1988). [2] M. Golubitsky and I. Stewart, ³Hopf Bifurcation with Dihedral Group Symmetry: Coupled Nonlinear Oscillators,² in Multiparameter Bifurcation Theory, Contemporary Mathematics, edited by M. Golubitsky and J. Guckenheimer (American Mathematical Society, Providence, 1986), Vol. 56, pp. 131-173. [3] M. Golubitsky and D. Shaeffer, Singularities and Groups in Bifurcation Theory, vol. I (Springer-Verlag, New York, 1988). Lou Pecora, email: pecora@anvil.nrl.navy.mil Naval Research Laboratory, Washington, D.C. 20375-5000, U.S.A. == My comments are my own and do not reflect the views of the U.S. Navy. == == No Spamming or solicitations -- both are illegal at this site == -------------------------------------------------------------------- Check out our Nonlinear Dynamics Web site: http://chaos-mac.nrl.navy.mil/ -------------------------------------------------------------------- * The 5th Experimental Chaos Conference Orlando FL June 1999. Check it out at http://www.physics.gatech.edu/ecc5/ * The 4th Experimental Chaos Conference Sessions & Abstracts Online: http://natasha.umsl.edu/Exp_Chaos4, proceedings available. --------------------------------------------------------------------