All Questions

Because flowmaps are homeomorphic maps, I was wondering if there is any literature that proves that diffeomorphism $\Phi(x)$ can be expressed as a flowmap of a certain dynamical system? that is, does ...

Let $x \in R^n$ and $f : R^n \to R^n$, $f\in C^1$ $$ \frac{\mathrm{d}}{\mathrm{d}t} x(t) = f(x(t)) $$ be such that $f(0) = 0$ is asymptotically stable. The domain of attraction is the set of initial ...

This problem may be an embarrassing one, but I could not prove it even for the $1$ dimensional case. Here is the problem: Question 1. $M$ is a compact $n$-dimensional smooth manifold in $R^{n+1}$. ...

Here a question that has me stumped. Maybe someone familiar with algebraic or differential curves can help. Suppose that $\gamma:[0,1] \rightarrow \mathbb{C}$ is an analytic function. Is it true ...