M E28

Standard bifurcation theory is concerned with families of vector elds involving one or several constant real parameters. The constant parameter provides a foliation of the total phase space. Frequently the presence of a trivial equilibrium manifold is also imposed. Bifurcation without parameters, in contrast, discards the foliation by a constant parameter. Only the trivial equilibrium manifold is preserved. A rich dynamic phenomenology arises when normal hyperbolicity of the trivial equilibrium fails, due to zero or purely imaginary eigenvalues. Specically, we address Hopf bifurcation, Takens-Bogdanov bifurcation, and Takens-Bogdanov bifurcation with additional time reversal symmetries, all in absence of parameters. We illustrate consequences of our results with examples from ordinary and partial dierential equations arising in systems of coupled oscillators, in the analysis and numerics of hyperbolic conservation and balance laws, and in the uid dynamics of plane Kolmogorov ows. The results are joint work with Andrei Afendikov, James C. Alexander, and Stefan Liebscher. For references see http://dynamics.mi.fu-berlin.de/

Kaffee/Tee: 16.45 Uhr in Raum M 614

Prof. Dr. Bernold Fiedler

FU Berlin