Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$

Abstract

We classify global bifurcations in generic one-parameter local families of \vfs on $S^2$ with a parabolic cycle. The classification is quite different from the classical results presented in monographs on the bifurcation theory. As a by product we prove that generic families described above are structurally stable.

arXiv comment26 pages, 8 figures