Non-universality of period-doubling bifurcations
in 3-d conservative reversible mappings
S. Komineas
Department of Physics, University of Crete,
P.O. Box 2208, GR--710.03 Heraklion, Crete, Greece
and Research center of Crete.
M. N. Vrahatis and T. Bountis
Department of Mathematics, University of Patras,
GR--261.10 Patras, Greece.
Abstract
Infinite sequences of period-doubling bifurcations are known to occur
generically (i.e. with codimension 1) not only in dissipative 1-D
systems but also in 2-D conservative systems, described by
area-preserving mappings. In this paper, we study a 3-D
volume-preserving, reversible mapping and show that it does possess
period- 2m, (m=1,2,...) orbits, with stability intervals whose
length decreases rapidly, with increasing m. Varying one
parameter of the system, however, we find that these orbits cannot be made
to bifurcate out of one another with the usual stability exchange
and universal properties of a period-doubling sequence. We thus
conjecture that such bifurcation sequences are not universal
(at least with codimension 1) in 3-D volume-preserving mappings,
or periodically driven 3-D conservative flows.