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Generalized Characteristics Of A Generic Polytope, Tommy Naugle

Electronic Theses and Dissertations

For a smooth hypersurface S ⊂ R 2n given by the level set of a Hamiltonian function H, a symplectic form ω on R2n induces a vector field XH which flows tangent to S. By the nondegeneracy of ω, there exists a distinguished line bundle LS whose characteristics are the integral curves of XH. When S is the boundary of a smooth convex domain K˜ ⊂ R 2n, then the least action among closed characteristics of LS is equal to the Ekeland-Hofer-Zehnder capacity, a symplectic invariant. From a result due to Artstein-Avidan and Ostrover, there exists a continuous extension of …