4 problems

Let $n$ be the degree parameter of the real polynomial Hamiltonian system … has no isochronous centers. At present, this conjecture remains open; recent developments are reported b…

Let $d\in\mathbb{N}^*$ with $d\geq 2$, and let $X$ be a polynomial vector field of degree $d$. An isochronous condition has geometric complexity $(q,m)$ if it admits a representati…

Let $X$ be a real polynomial Hamiltonian vector field … where $H(x,y)$ is a real polynomial in $x$ and $y$. The degree of $X$ is the maximum of the degrees of $\partial_xH$ and…

Isochronicity conjecture. The system has an isochronous center at $0$. Isochronous centers are centers whose nearby periodic orbits have a common period; determining them for plana…