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Query: faculty: "FNWI" and publication year: "2007"

AuthorsA.J. Homburg, T. Young
TitleIntermittency and Jakobson's theorem near saddle-node bifurcations
JournalDiscrete and Continuous Dynamical Systems (DCDS) - Series A
Volume17
Year2007
Issue1
Pages21-58
ISSN10780947
FacultyFaculty of Science
Institute/dept.FNWI: Korteweg-de Vries Institute for Mathematics (KdVI)
AbstractAbstract. We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. We show that there is a parameter set of positive but not full Lebesgue 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.
Document typeArticle
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