Dynamical arguments are presented which suggest that there are non-integrable systems without clustering of singularities, without infinite singularities, or singularities with an infinite number of branches in the complex t-plane. Several examples with only algebraic singularities are studied, for which strong numerical evidence is presented for non-integrability and infinitely sheeted solutions. 'Weak-Painleve' potentials are also analysed from this point of view, and all integrable cases are found to possess only finitely sheeted solutions.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)