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Aug 31, 2010 at 23:05 comment added Robert Bruner This is the example I had remembered from years ago, but the source I got it from did not make its exact meaning clear. Hartman's C^1 linearization is sufficient to exclude the sort of pathology I was worried about above and allows me to finish off something I set aside years ago! Apparently I missed this in Hartman's 1960 paper. Thank you.
Aug 31, 2010 at 22:34 vote accept Robert Bruner
Aug 30, 2010 at 7:15 comment added Hans Lundmark To be precise, I should of course of course have said "any $C^2$ planar flow is $C^1$ linearizable at a hyperbolic equilibrium" (but that was sort of clear from the question).
Aug 30, 2010 at 7:09 history answered Hans Lundmark CC BY-SA 2.5