Wednesday, May 3, Lori Student Center, Room 228, 3pm

About the occurence of robust heteroclinic cycles in hydrodynamical systems with symmetry

Pascal Chossat
Institut Nonlinear
Universite de Nice, France

Robust heteroclinic cycles are a common phenomenon in systems with symmetry and their bifurcation from a trivial state has been much studied since the seminal works of Guckenheimer and Holmes (1988), and Ambruster, Guckenheimer and Holmes (1988). There existence is however subjected to a number of conditions (including, in certain cases, non-generic conditions), which are met in certain hydrodynamical systems, as it has been early recognized by Proctor and Jones (1988). It turns out that these conditions are in fact satisfied by a wide class of hydrodynamical systems, and more generally by systems the nonlinearity of which is quadratic and of advective type. I will explain this fact and illustrate it on systems with spherical symmetry, as was done by Chossat and Guyard (1997).
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