Erratum: Alternating period-doubling cascades
نویسندگان
چکیده
منابع مشابه
Period-doubling cascades galore
Period-doubling cascades for the quadratic family are familiar to every student of elementary dynamical systems. Cascades are also often observed in both numerical and scientific experiments. Yet in all but the simplest cases, very little is known about why they exist. When there is one cascade, there are almost always infinitely many. Further, there has been no systematic way of distinguishing...
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We consider perturbations of the Feigenbaum map in n dimensions. In the analytic topology we prove that the maps that are accumulated by period doubling bifurcations are approximable with homoclinic tangencies. We also develop a n-dimensional Feigenbaum theory in the Cr topology, for r large enough. We apply this theory to extend the result of approximation with homoclinic tangencies for Crmaps...
متن کاملPeriod-doubling cascades for large perturbations of Hénon families
The Hénon family has been shown to have period-doubling cascades. We show here that the same occurs for a much larger class: Large perturbations do not destroy cascades. Furthermore, we can classify the period of a cascade in terms of the set of orbits it contains, and count the number of cascades of each period. This class of families extends a general theory explaining why cascades occur [5].
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2013
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/26/9/2745