Finitely and infinitely sheeted solutions in some classes of nonlinear ODEs (Q1302434)

The authors deal with a simple class of ODEs of the form \[ x'= x-x^n+ \varepsilon g(t), \qquad x\in \mathbb{C}, \quad n\in \mathbb{N}, \] possessing only algebraic singularities. In this case the authors examine a distinction between integrable \(g(t)=1\) and non-integrable \(g(t)=t\) ODEs, based on the solutions that are globally finitely sheeted. Using asymptotic formulas the authors show the difference in the formation of the singularity patterns, as well as the existence of non-dense vs. dense singularity structures. The authors also provide a numerical simulation of the theoretical results.