Renormalisation in a circle map with two inflection points

Abstract

An extended version of the sine circle map becomes non-invertible by developing simultaneously two critical points in part of parameter space. Universality in the corresponding transition from quasiperiodicity to chaos manifests itself in the organisation of doubly superstable orbits. Four operators are needed to generate all such orbits. The existence of non-trivial equivalence relations for operation sequences makes the present theory different from other multi-operator renormalisation approaches. Possible implications of the theory in higher-dimensional systems are discussed.