Pure Maths Colloquium: The principle of minimal action in Hamiltonian dynamics.
2 May 2011 17:15 in CM221
In this talk, I intend to illustrate how the principle of minimal action can be used to obtain more information on the dynamics of convex Hamiltonian systems and their symplectic nature.
Starting from the crucial observation that orbits on invariant Lagrangian graphs can be characterised in terms of their 'action-minimizing properties', I'll discuss how analogue features can be traced in a more general setting, namely the so-called 'Tonelli Hamiltonian systems'. This different point of view brings to light a plethora of compact invariant subsets of the system that, under many points of view, could be considered a generalisation of invariant Lagrangian graphs, despite not being in general either submanifolds or regular. I shall describe their structure and their symplectic properties, as well as their relation to the dynamics of the system.
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