On the cohomological equation for nilflows
Livio Flaminio, Giovanni Forni
Abstract
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 Dn such that any sufficiently smooth function g is a coboundary iff it belongs to the kernel of all the distributions Dn.
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