A generalization of the Unstable Periodic Orbits and its role in the transport in Hamiltonian systems

December 13, 2022, 1:15 p.m. (CET)

Seminar: Topical Issues of Theoretical Physics

Time: December 13, 2022, 1:15 p.m. (CET)
Lecturer: Francisco Gonzalez Montoya (University of Leeds, UK)
Venue: Universität Stuttgart, Raum 4.331 (NWZ II), Pfaffenwaldring 57, Stuttgart-Vaihingen
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In a 2 degree of freedom Hamiltonian system, the dynamics around a saddle point in the potential energy is determined by the unstable Hyperbolic Periodic Orbit and its invariant manifolds associated with the saddle. Using the Periodic Orbit it is possible to calculate the flux through the saddle for a given energy. For multidimensional potential energy surfaces with index one saddles, it is possible to construct a generalization of the Hyperbolic Periodic Orbits called Normally Hyperbolic Invariant Manifold (NHIM). This geometrical object plays an analogous role to the Unstable Periodic Orbit. In this talk, we present the basic construction of a multidimensional NHIM and illustrate its bifurcations in one 3 degree of freedom example. The system considered is a charge in the perturbed magnetic field of a dipole.

Institut für Theoretische Physik
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