منابع مشابه
Circle Maps , Rotation Numbers
A lecture given at the Department of Biology, University of Oslo, at the \population dynamics seminar" 27.11.98.
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We consider strong and weak topologies on the space of orbits from the unit interval to the set of probability measures on a given domain. In particular, we are interested in periodic orbits of probability measures on the circle. We show that a real-valued rotation number can be defined in a natural way for all smooth enough orbits whose range is composed of probability measures supported on th...
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Rotation numbers have played a central role in the study of (unforced) monotone circle maps. In such a case it is possible to obtain a priori bounds of the form »¡ 1=n μ ...1=n†...yn ¡ y0† μ »‡ 1=n, where ...1=n†...yn ¡ y0† is an estimate of the rotation number obtained from an orbit of length n with initial condition y0, and » is the true rotation number. This allows rotation numbers to be com...
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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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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2013
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236198.2012.719501