Rods, spheres and balls from a Hamiltonian system perspective

07.12.2016, 15:00  –  Haus 9, Raum 2.22
Institutskolloquium

Alberto Abbondandolo (Ruhr Universität Bochum), Nils Waterstraat (University of Kent)

• 15:00 Uhr Alberto Abbondandolo "On short geodesics and shadows of balls"
• 16:00 Uhr Teepause
• 16:30 Uhr Nils Waterstraat  "The buckling of the Euler rod"

   

Alberto Abbondandolo (Ruhr Universität Bochum)

On short geodesics and shadows of balls

How large is the four-dimensional shadow of a symplectic ball? And how long can the shortest closed geodesic on a two-sphere be? After introducing the necessary background, I will show how these two questions can be put into a common framework using a particular class of Hamiltonian dynamical systems known as Reeb flows.

Nils Waterstraat (University of Kent)

The buckling of the Euler rod

Columns fail by buckling when their critical load is reached, a phenomenon that can be explained in the framework of bifurcation  theory, which attempts to explain various phenomena that have been  discovered and described in the natural sciences over the centuries. Another classical example is the appearance of Taylor vortices, and often Hamiltonian systems play a central role.

Mathematically speaking, bifurcation theory is a field of nonlinear  analysis that studies branches of solutions of equations of the type  $F(\lambda,x)=0$, where $F:[0,1]\times X\rightarrow Y$ is a continuous  map and $X,Y$ are real Banach spaces.

The aim of this talk is to show that concepts of global analysis, like the spectral flow, can be used to investigate bifurcation phenomena. Moreover, we discuss an application to bifurcation of periodic orbits of Hamiltonian systems.