Dayal Strub (University of Warwick, UK)
Morse bifurcations of transition states
A transition state for a Hamiltonian system is a closed, invariant, codimension-2 submanifold of an energy-level, that can be spanned by two compact codimension-1 surfaces of unidirectional, locally minimal flux whose union locally separates the energy-level. This union, called a dividing surface, can be used to find an upper bound on the rate of transport in Hamiltonian systems. After recalling the basic transport scenario about an index-1 critical point of the Hamiltonian, with transition states diffeomorphic to spheres for energies just above the critical one, we shall ask what qualitative changes in the transition state may occur as the energy is increased further. We will find that there is a class of systems for which the transition states change diffeomorphism class via Morse bifurcations, and consider a number of examples.
This is joint work with Robert MacKay.