at the moment i read the following paper:
https://arxiv.org/pdf/1512.04436v1.pdf
I have some questions about it and i hope someone can help me. On page 4/5 they introduce isochrons and the isochron map. What is the meaning of $\mathbb{R}\bmod T$ ? In other literature, they use $[0,T)$, $S^1$ or the quotient space $\mathbb{R}/\mathbb{Z}$ (or $\mathbb{R}/T\mathbb{Z}$). But
if it means $[0,T)$, i cant see that the isochron map is $C^k$. Isn´t there a problem with the total derivative at $x\in W $ with $\theta(x)=0$?
if it means $S^1$ then the dimensions of e.g. the Hessian matrix doesnt fit in the context (see page 6, Theorem 2 .3 (2.19)).
if it means $\mathbb{R}/\mathbb{Z}$. How can i get the Hessian matrix?
Note that they use modT in (2.13).
Thanks, Sebastian.