منابع مشابه
The Doubling Map with Asymmetrical Holes
Let 0 < a < b < 1 and let T be the doubling map. Set J (a, b) := {x ∈ [0, 1] : Tx / ∈ (a, b), n ≥ 0}. In this paper we completely characterize the holes (a, b) for which any of the following scenarios holds: (i) J (a, b) contains a point x ∈ (0, 1); (ii) J (a, b) ∩ [δ, 1− δ] is infinite for any fixed δ > 0; (iii) J (a, b) is uncountable of zero Hausdorff dimension; (iv) J (a, b) is of positive ...
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We investigate the escape dynamics of the doubling map with a time-periodic hole. Ulam's method was used to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the sides of the hole are moving in or out of phase respectively. We find out that the escape rate is well described by the overlap of the hole with its images, ...
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Given a countable set X (usually taken to be N or Z), an infinite permutation π of X is a linear ordering ≺π of X , introduced in [6]. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of uniformly recurrent aperiodic binary words under the letter doubling map. An upper bound for the complexity is found for general words, and a formula ...
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We study the motion of light in the gravitational field of two Schwarzschild black holes, making the approximation that they are far apart, so that the motion of light rays in the neighborhood of one black hole can be considered to be the result of the action of each black hole separately. Using this approximation, the dynamics is reduced to a two-dimensional map, which we study both numericall...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2013
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2013.98