| Abstract: | In this paper, we shall prove that Axiom A maps are dense in the space of C2 interval maps (endowed with the C2 topology). As a step of the proof, we shall prove real and complex a priori bounds for (first return maps to certain small neighborhoods of the critical points of) real analytic multimodal interval maps with non-degenerate critical points. We shall also discuss rigidity for interval maps without large bounds. Mathematics Subject Classification (2000) Primary 37E05; Secondary 37F25 |
