CONNECTING PERIOD-DOUBLING CASCADES TO CHAOS
نویسندگان
چکیده
منابع مشابه
Connecting Period-Doubling Cascades to Chaos
The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a parameter often reveal a complicated intermingling of period-doubling cascades and chaos. Period doubling can be studied at three levels of complexity. The fi...
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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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Period-doubling cascades are among the most prominent features of many smooth one-parameter families of maps, F : R×M → M, where M is a locally compact manifold without boundary, typically R . In particular, we investigate F (μ, ·) for μ ∈ J = [μ1, μ2], when F (μ1, ·) has only finitely many periodic orbits while F (μ2, ·) has exponential growth of the number of periodic orbits as a function of ...
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ژورنال
عنوان ژورنال: International Journal of Bifurcation and Chaos
سال: 2012
ISSN: 0218-1274,1793-6551
DOI: 10.1142/s0218127412500228