Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouville domains from Okounkov bodies   Given a strictly concave rational PL function $\phi$ on a complete
$n$-dimensional fan $\Sigma$, we construct an exact symplectic structure of
finite volume on $(\mathbb{C}^\times)^n$ and a family of functions
$H_{\phi,\epsilon}$ called polyhedral Hamiltonians. We prove that for each
$\epsilon$ the one-periodic orbits of $H_{\phi,\epsilon}$ come in families
corresponding to finitely many primitive lattice points of $\Sigma$ and
determine their topology. When $\phi$ is negative on the rays of $\Sigma$, we
show that the level sets of polyhedral Hamiltonians are hypersurfaces of
contact type. As a byproduct, this construction provides a dynamical model for
the singularities of toric varieties obtained as degenerations of Fano
manifolds in any dimension via Okounkov bodies.

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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con