Higher bifurcation currents, neutral cycles and the Mandelbrot set
نویسندگان
چکیده
منابع مشابه
Higher bifurcation currents, neutral cycles and the Mandelbrot set
We prove that given any θ1, . . . , θ2d−2 ∈ R\Z, the support of the bifurcation measure of the moduli space of degree d rational maps coincides with the closure of classes of maps having 2d − 2 neutral cycles of respective multipliers e1 , . . . , e2d−2 . To this end, we generalize a famous result of McMullen, proving that homeomorphic copies of (∂M) are dense in the support of the k-bifurcatio...
متن کاملHypercomputing the Mandelbrot Set?
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...
متن کاملIs the Mandelbrot set computable?
We discuss the question whether the Mandelbrot set is computable. The computability notions which we consider are studied in computable analysis and will be introduced and discussed. We show that the exterior of the Mandelbrot set, the boundary of the Mandelbrot set, and the hyperbolic components satisfy certain natural computability conditions. We conclude that the two–sided distance function ...
متن کاملInstability of the Mandelbrot Set
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...
متن کاملΠ in the Mandelbrot Set
The Mandelbrot set is arguably one of the most beautiful sets in mathematics. In 1991, Dave Boll discovered a surprising occurrence of the number π while exploring a seemingly unrelated property of the Mandelbrot set. Bolls Þnding is easy to describe and understand, and yet it is not widely known possibly because the result has not been rigorously shown. The purpose of this paper is to prese...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2014
ISSN: 0022-2518
DOI: 10.1512/iumj.2014.63.5328