If $X$ is a Hausdorff space, by a flow I mean a continuous surjection $F: X \times \mathbb{R} \rightarrow X$ such that $F(x, s + t) = F(F(x,s), t)$ for all $x \in X$ and $s, t \in \mathbb{R}$. If $x$ is periodic (or fixed) under $F$, then let $p_F(x)$ denote the minimal non-negative time such th...

In the attached figures, we have two kinds of curves; 1- a big closed curve which is somehow a limaçon. 2- many ellipses which are the same by the formula but different by the center. By putting some rotate and translated elliple, that is $$4\big(\frac{u}{\tau}\big)^2+\frac{13}{16}\big(\frac{v+\f...