Binary tree approach to scaling in unimodal maps
نویسندگان
چکیده
منابع مشابه
Bifurcations of Unimodal Maps
We review recent results that lead to a very precise understanding of the dynamics of typical unimodal maps from the statistical point of view. We also describe the (generalized) renormalization approach to the study of the statistical properties of typical unimodal maps.
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We describe up to conjugacy all unimodal and bimodal maps that are chaotic, by giving necessary and sufficient conditions for unimodal and bimodal maps of slopes ±s to be transitive.
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Examples are given of tent maps T for which there exist nontrivial sets B ⊂ [0, 1] such that T : B → B is a homeomorphism.
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The universal period-doubling scaling of a unimodal map with an asymmetric critical point is governed by a period-2 point of a renormalisation operator. The period-2 point is parametrised by the degree of the critical point and the asymmetry modulus. In this paper we study the asymptotics of period-2 points and their associated scaling parameters in the singular limit of degree tending to 1.
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Robust chaos occurs when a dynamical system has a neighborhood in parameter space such that there is one unique chaotic attractor, and no periodic attractors are present [Barreto et al., 1997; Banerjee et al., 19981. This behavior, expected to be relevant for any practical applications of chaos, was shown to exist in a general family of piecewise-smooth twodimensional maps, but conjectured to b...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 1994
ISSN: 0022-4715,1572-9613
DOI: 10.1007/bf02186875