On the Finiteness of Attractors for One-Dimensional Maps with Discontinuities

Abstract

Since the proof, at the end of the 80's, of the finiteness of the number of attractors for $C^3$ maps of the interval having negative Schwarzian derivative, it has been generally considered that the same result could be true for maps with discontinuities. In the present paper we show that this is indeed the case.

arXiv comment33 pages, 8 figures