Contents 
Let $\phi:\mathbb{R}\times M\to M$ be a nonsingular continuous dynamical system defined on a differentiable $n$manifold $M$. If $\phi$ is generated by a $C^1$ vector field, then $M$ can be covered with flow boxes $D^{n1}\times I$ on which $\phi$ is a local flow along the $I$fibers and $D^{n1}$ is the $(n1)$ disk. This in general is not the case for $n >3$. In 1957, R.H.~Bing gave an example of a generalized 3manifold, which is not homeomorphic to $\mathbb{R}^3$, but its product with $\mathbb{R}^1$ is
homeomorphic to $\mathbb{R}^4$. Thus there is a $C^0$ dynamical system defined on $\mathbb{R}^4$ not admitting flow boxes.
We consider the feasibility of defining generalized flow boxes and their applications. 
