Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous limits of generalized pentagram maps   We provide a rigorous treatment of continuous limits for various
generalizations of the pentagram map on polygons in $\mathbb{RP}^d$ by means of
quantum calculus. Describing this limit in detail for the case of the
short-diagonal pentagram map, we verify that this construction yields the
$(2,d+1)$-KdV equation, and moreover, the Lax form of the pentagram map in the
limit is proved to become the Lax representation of the corresponding KdV
system. More generally, we introduce the $\chi$-pentagram map, a geometric
construction defining curve evolutions by directly taking intersections of
subspaces through specified points. We show that its different configurations
yield certain other KdV equations and provide an argument towards disproving
the conjecture that any KdV-type equation can be discretized through
pentagram-type maps.

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph