Dynamics of acyclic interval maps
Published Web Locationhttps://doi.org/10.1007/s11784-009-0115-8
We investigate conditions under which a map in a possibly noncompact interval is acyclic--- the only periodic points are fixed points. Several earlier results are generalized to maps with multiple fixed points. The chief tools are convergence results due to Coppel and Sharkovski, and the Schwarzian derivative. Illustrative examples are given and open problems are suggested.