Homeomorphisms between limbs of the Mandelbrot set
نویسندگان
چکیده
منابع مشابه
Homeomorphisms between Limbs of the Mandelbrot Set
Using a family of higher degree polynomials as a bridge, together with complex surgery techniques, we construct a homeomorphism between any two limbs of the Mandelbrot set of common denominator. Induced by these homeomorphisms and complex conjugation we obtain an involution between each limb and itself, whose fixed points form a topological arc. All these maps have counterparts at the combinato...
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Using holomorphic surgery techniques, we construct a homeomorphism between a neighborhood of any limb without root point of the Mandelbrot set and a neighborhood of any other of equal denominator, in such a way that the limbs are mapped to each other. On the limbs, the homeomorphism coincides with that constructed in “Homeomorphisms between limbs of the Mandelbrot set” (J. Geom. Anal. 9 (1999),...
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On subsets of the Mandelbrot set, EM ⊂M, homeomorphisms are constructed by quasi-conformal surgery. When the dynamics of quadratic polynomials is changed piecewise by a combinatorial construction, a general theorem yields the corresponding homeomorphism h : EM → EM in the parameter plane. Each h has two fixed points in EM , and a countable family of mutually homeomorphic fundamental domains. Po...
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The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the (non-)computability of the set. It considers two models of decidability over the reals (which are treated much more thoroughly and technically in [1], [2], [3] and [4] amon...
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für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-11047-5