منابع مشابه
On Fibers and Renormalization of Julia Sets and Multibrot Sets
We continue the description of Mandelbrot and Multibrot sets and of Julia sets in terms of fibers which was begun in [S3] and [S4]. The question of local connectivity of these sets is discussed in terms of fibers and becomes the question of triviality of fibers. In this paper, the focus is on the behavior of fibers under renormalization and other surgery procedures. We show that triviality of f...
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We give new proofs that the Mandelbrot set is locally connected at every Misiurewicz point and at every point on the boundary of a hyperbolic component. The idea is to show “shrinking of puzzle pieces” without using specific puzzles. Instead, we introduce fibers of the Mandelbrot set (see Definition 3.2) and show that fibers of certain points are “trivial”, i.e., they consist of single points. ...
متن کاملA count of maximal small copies in Multibrot sets
We give a recursive formula to count maximal small copies of the Mandelbrot set and its higher degree analogues. This formula is used to compute the asymptotic growth of the number of maximal small copies of period n. Mathematics Subject Classification: 37F20
متن کاملLevel Sets of Functions and Symmetry Sets of Surface Sections
We prove that the level sets of a real C function of two variables near a non-degenerate critical point are of class C [s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at an elliptic or hyperbolic point, and in particular at an umbilic point. We go on to use the results to study symmetry sets of the planar sections. We also anal...
متن کاملCross sections at HERA
The energy dependence of a given process teaches us about the dynamics of this process. If the energy dependence can be described by a Reggetype approach a la Donnachie and Landshoff [1] we call the process soft. The total hadron-proton cross sections dependence on center-of-mass energy exemplifies the behaviour of soft processes.. If the energy dependence can be described by perturbative QCD (...
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ژورنال
عنوان ژورنال: The Journal of Analysis
سال: 2016
ISSN: 0971-3611,2367-2501
DOI: 10.1007/s41478-016-0010-9