We study period-doubling bifurcations in periodically driven two-dimensional flows, which are measure-preserving. We demonstrate on several examples, that this important bifurcation sequence proceeds very similarly and with the same universal constants, as in the Hamiltonian case of two degrees of freedom. This is explained by the fact that the Poincaré map of our models, upon return to any point of their periodic orbits, is (locally) area-preserving, a result which suggests an equivalence of all measures for such bifurcation phenomena in measure-preserving systems.
ASJC Scopus subject areas
- Physics and Astronomy(all)