Period doubling
نویسندگان
چکیده
منابع مشابه
Lacunarity and Period-doubling
We show that the deviation from power laws of the scaling of chaotic measures such as Lyapunov exponents and topological entropy is periodic in the logarithm of the distance from the accumulation of period doubling. Moreover, this periodic function is asymptotically universal for each measure (for functions in the appropriate universality class). This is related to the concept of lacunarity kno...
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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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The period doubling renormalization operator was introduced by M. Feigenbaum and by P. Coullet and C. Tresser in the nineteen-seventieth to study the asymptotic small scale geometry of the attractor of one-dimensional systems which are at the transition from simple to chaotic dynamics. This geometry turns out to not depend on the choice of the map under rather mild smoothness conditions. The ex...
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We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point. Similar techniques then allow us to show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable with the diameters of all periodic intervals going to zero as the period goes t...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2014
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.3958