arXiv subjects
Publications and source records attributed to Jean-Marie Strelcyn.
Recently A.R.Chouikha gave a new characterization of isochronicity of center at the origin for the equation $x"+g(x)=0$, where $g$ is a real smooth function defined in some neighborhood of $0 \in \R$. We describe another proof of his characterization and some new development of the subject.
We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $$\dot x=-y+A(x,y),\;\dot y=x+B(x,y),$$ where $A,\;B\in \mathbb{R}[x,y]$, which can be reduced to the Liénard type equation. When $deg(A)\leq 4$ and $deg(B) \leq 4$, using the so-called C-algorithm we found $36$ new families of isochronous centers. When the Urabe function $h=0$ we provide an explicit general formula for linearization. This paper is a direct continuation of \cite{BoussaadaChouikhaStrelcyn2010} but can be read independantly.
We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $\dot x=-y+A(x,y), \dot y=x+B(x,y)$, where $A, B\in \mathbb{R}[x,y]$, which can be reduced to the Lienard type equation. Using the so-called C-algorithm we have found 27 new multiparameter isochronous centers.
It is proved that the Halphen system of ordinary differential equations has no non-trivial rational first integrals.