7 votes

Are there general solutions to quadratic, 2D, continuous, time-invariant dynamical systems?

A useful search phrase is “quadratic planar vector fields”. Despite much research, there are still many open problems concerning such systems. For example, Hilbert's sixteenth problem asks for an ...
Hans Lundmark's user avatar
2 votes

Examples of specific points $g\in G:=\text{SL}(2,\mathbb R)$ such that the curve $u_tg \Gamma, \Gamma:=\text{SL}(2,\mathbb Z)$ is dense in $G/\Gamma$?

If you want a specific matrix $g$, you can take $$ g=\left[ \begin{array}{cc} 1&0\\ \sqrt{2}&1\end{array}\right]. $$ Here is the reason. Let $U_\infty$ denote the subgroup of strictly upper ...
Moishe Kohan's user avatar
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