- 01-195 Ale Jan Homburg Todd Young
- Jakobson's Theorem near saddle-node bifurcations
May 29, 01
(auto. generated ps),
of related papers
Abstract. We discuss one parameter families of unimodal maps,
with negative Schwarzian derivative, unfolding a
It was previously shown that for a parameter set of positive
Lebesgue density at the bifurcation, the maps possess
attracting periodic orbits of high period.
We show that there is also a parameter set of positive
density at the bifurcation, for which
the maps exhibit absolutely continuous
invariant measures which are supported on the largest possible
interval. We prove that these measures converge weakly to
an atomic measure supported on the orbit of the saddle-node point.
Using these measures we analyze the intermittent time series that result
from the destruction of the periodic attractor
in the saddle-node bifurcation and prove
asymptotic formulae for the frequency with which
orbits visit the region previously occupied by the periodic attractor.