On the cohomological equation for nilflows
Livio Flaminio - UFR de MathÃ©matiques, UniversitÃ© de Lille 1 (USTL), F59655 Villeneuve d'Asq Cedex, France (email) 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 $g: M\to \mathbb{R}$ is a coboundary for the flow generated by $X$, i.e., when there exists a function $f: M\to \mathbb{R}$ 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 $D_n$.
Keywords: Nilflows, Cohomological Equations.
Received: March 2006; Available Online: October 2006. |