Feigenbaum theory for unimodal maps with asymmetric critical point: rigorous results (Q1290459)

The subject of this paper deals with functional equations of the Feigenbaum type which occur in the theory of period-doubling cascades for families of unimodal maps \(f\) of an interval with a single critical point of degree \(d\) and which has differing left and right \(d\)-th derivative at a critical point. The authors apply the methods of H. Epstein to prove the existence of a line of period-2 solutions of the Feigenbaum period-doubling renormalisation transformation. These solutions govern the universal behaviour of families of unimodal maps with ``asymmetric critical points'' of degree \(d\).