|Time:||June 27, 2023, 1:15 p.m. (CEST)|
|Lecturer:||Christof Jung (Universidad Nacional Autónoma de México)|
|Venue:||Universität Stuttgart, Raum 4.331 (NWZ II), Pfaffenwaldring 57, Stuttgart-Vaihingen
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For Hamiltonian systems with 3 degrees of freedom the Poincaré map has a 4-dimensional domain. The most important invariant subsets in this map are 2-dimensional normally hyperbolic invariant surfaces (NHIMs). In the phase space they sit over the index-1 saddle points of the effective potential. The stable and unstable manifolds of the NHIMs build up a homoclinic/heteroclinic tangle in the map. It is the 4-dimensional generalization of the well known horseshoes in 2-dimensional Poincaré maps.
As an example of demonstration we study the motion of a test particle in the effective potential of a rotating barred galaxy. In this example we encounter surprising connections between the phase space structures of the model and observable structures in the galaxies.