Topological obstructions to smoothness for infinitely renormalizable maps of the disc
Topological obstructions to smoothness for infinitely renormalizable maps of the disc
We analyse the signature type of a cascade of periodic orbits associated with period-doubling renormalizable maps of the two-dimensional disc. The signature is a sequence of rational numbers invariant with respect to orientation-preserving topological conjugacies, which describes how periodic orbits are linked around each other. We prove that in the …