April 13, 2007
Federica Pasquotto (Amsterdam): Closed characteristics on non-compact hypersurfaces in R2n
Abstract:
Compact hypersurfaces, in 2n-dimensional Euclidean space, arising as
regular energy level sets of mechanical Hamiltonian functions are of
contact type. Therefore, by Viterbo's theorem, they always carry a
closed characteristic.
In the non-compact case, mechanical hypersurfaces still satisfy the
contact type condition, but they do not need to carry any closed
characteristic, as some simple examples can show. In other words,
additional conditions are needed to make up for the lack of compactness.
In this talk I will discuss a set of very "natural" geometric and
topological assumptions for the non-compact setting and describe how
these provide a complete existence result (joint work with R.
Vandervorst and J.B. van den Berg).
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