A classification of explosions in dimension one

Abstract

A discontinuous change in the size of an attractor is the most easily observed type of global bifurcation. More generally, an explosion is a discontinuous change in the set of recurrent points. An explosion often results from heteroclinic and homoclinic tangency bifurcations. Newhouse and Palis conjectured in 1976 that planar explosions are generically the result of either tangency or saddle node bifurcations. In this paper, we prove this conjecture for one-dimensional maps. Furthermore, we give a full classification for all possible tangency bifurcations and whether they lead to explosions.