Period Doubling and the Lefschetz Formula


This article gives an application of the Lefschetz fixed point theorem to prove, under certain hypotheses, the existence of a family of periodic orbits for a smooth map. The family has points of periods 1 p for some p and all k > 0. There is a version of the result for a parametrized family /t which shows that these orbits are "connected" in parametrized… (More)