Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Oberseminar Differentialgeometrie

 

Professor Dr. Alain Chenciner
Universität Paris Diderot und Pariser Observatorium

 
spricht am
 
Montag, 22. Januar 2018
 
um
 
16:00 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Perturbing a planar rotation : normal hyperbolicity and angular twist«

Abstract:
Perturbing the germ at the origin of a planar rotation re2πiθ → re2πi(θ+ω) leads to two celebrated results which describe the dynamical behaviour of the iterates of the perturbed diffeomorphism F , that is the structure of the orbits O(z) = {z, F (z), F 2(z), . . . , F n(z), . . .}: the Andronov-Hopf- Naimark-Sacker bifurcation of invariant curves under a generic radial hy- pothesis of weak attraction (or repulsion) and the Moser invariant curve theorem under an angular twist hypothesis in the area preserving case. The invariant curves whose existence is proved are normally hyperbolic with generic induced dynamics in the first case, with a dynamics smoothly conjugated to a diophantine rotation in the second one. In generic 2- parameter families of germs of diffeomorphisms of the plane near a fixed point, the tension between radial and angular (or hyperbolic and ellip- tic) behaviour leads to phenomena where the whole wealth of the area preserving situation is unfolded along some direction of the parameter space.

 

Hierzu ergeht herzliche Einladung.
Lei Zhao
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).



wwwadm@Math.Uni-Augsburg.DE,    Mi 25-Okt-2017 11:26:56 MESZ