Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the cohomological equation for nilflows   Let X be a vector field on a compact connected manifold M. An important
question in dynamical systems is to know when a function g:M -> R is a
coboundary for the flow generated by X, i.e. when there exists a function f:
M->R such that Xf=g. In this article we investigate this question for nilflows
on nilmanifolds. We show that there exists countably many independent Schwartz
distributions D_n such that any sufficiently smooth function g is a coboundary
iff it belongs to the kernel of all the distributions D_n.

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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci