A Necessary and Sufficient Condition for a Self-Diffeomorphism of a Smooth Manifold to be the Time-1 Map of the Flow of a Differential Equation

Abstract

In topological dynamics, one considers a topological space $X$ and a self-map $f:X\to X$ of $X$ and studies the self-map's properties. In global analysis, one considers a smooth manifold $M^n$ and a differential equation $\xi :M\to TM$ on $M$ and studies the flow ${\Phi }_t:M\times \mathbb{R}\to M$ of the differential equation. In this paper, we consider a necessary and sufficient condition for a self-diffeomorphism $f$ of a manifold $M$ to be the time-1 map ${\Phi }_1$ of the flow of a differential equation on $M$.

arXiv commentThis paper may be a little "light" on content and therefore not publishable; however, it doesn't hurt (I don't think) to upload it to the arXiv for comments. Having said that, I would greatly appreciate and and all comments on the paper