Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The geometry of dented pentagram maps   We propose a new family of natural generalizations of the pentagram map from
2D to higher dimensions and prove their integrability on generic twisted and
closed polygons. In dimension $d$ there are $d-1$ such generalizations called
dented pentagram maps, and we describe their geometry, continuous limit, and
Lax representations with a spectral parameter. We prove algebraic-geometric
integrability of the dented pentagram maps in the 3D case and compare the
dimensions of invariant tori for the dented maps with those for the higher
pentagram maps constructed with the help of short diagonal hyperplanes. When
restricted to corrugated polygons, the dented pentagram maps coincide between
themselves and with the corresponding corrugated pentagram map. Finally, we
prove integrability for a variety of pentagram maps for generic and partially
corrugated polygons in higher dimensions.

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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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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: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin