Geometry, Mechanics and Control Seminar

Structure preserving integration of boundary value problems with bifurcations

Speaker:  Christian Offen (Paderborn University, Germany)
Date:  Friday, 25 March 2022 - 15:30
Online:  us06web.zoom.us/j/7555463367 (ID: 755 546 3367)

Abstract:

Boundary value problems for Hamiltonian systems arise in the context of optimal control problems or the computation of conjugate loci, for instance. It is well known that symplectic numerical methods and variational integrators show excellent energy conservation in long term simulations of Hamiltonian dynamics. As boundary value problems are posed on intervals of fixed, moderate length, it is not immediately clear, whether structure preserving methods are advantageous in this context. Solutions to boundary value problems are not unique and can undergo bifurcations when parameters are present: for instance, two solutions can merge and annihilate one another as a parameter is varied. In this talk, I will show that structurally stable bifurcations of solutions to Hamiltonian boundary value problems can be classified and that structure preservation is important to correctly capture bifurcations numerically.
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