Homeomorphisms between limbs of the Mandelbrot set

Dzmitry Dudko; Dierk Schleicher

doi:10.1090/S0002-9939-2011-11047-5

Homeomorphisms between limbs of the Mandelbrot set

Dzmitry Dudko
, Dierk Schleicher

Mathematics

Constructor University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We prove that for every hyperbolic component of the Mandelbrot set, any two limbs with equal denominators are homeomorphic so that the homeomorphism preserves periods of hyperbolic components. This settles a conjecture on the Mandelbrot set that goes back to 1994.

Original language	English
Pages (from-to)	1947-1956
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	140
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-2011-11047-5
State	Published - 2012

Access to Document

10.1090/S0002-9939-2011-11047-5

Cite this

@article{df26afba3fd54adbb477fbc0ceebe8f5,

title = "Homeomorphisms between limbs of the Mandelbrot set",

abstract = "We prove that for every hyperbolic component of the Mandelbrot set, any two limbs with equal denominators are homeomorphic so that the homeomorphism preserves periods of hyperbolic components. This settles a conjecture on the Mandelbrot set that goes back to 1994.",

author = "Dzmitry Dudko and Dierk Schleicher",

year = "2012",

doi = "10.1090/S0002-9939-2011-11047-5",

language = "English",

volume = "140",

pages = "1947--1956",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

number = "6",

}

TY - JOUR

T1 - Homeomorphisms between limbs of the Mandelbrot set

AU - Dudko, Dzmitry

AU - Schleicher, Dierk

PY - 2012

Y1 - 2012

N2 - We prove that for every hyperbolic component of the Mandelbrot set, any two limbs with equal denominators are homeomorphic so that the homeomorphism preserves periods of hyperbolic components. This settles a conjecture on the Mandelbrot set that goes back to 1994.

AB - We prove that for every hyperbolic component of the Mandelbrot set, any two limbs with equal denominators are homeomorphic so that the homeomorphism preserves periods of hyperbolic components. This settles a conjecture on the Mandelbrot set that goes back to 1994.

UR - https://www.scopus.com/pages/publications/84857283572

U2 - 10.1090/S0002-9939-2011-11047-5

DO - 10.1090/S0002-9939-2011-11047-5

M3 - Article

AN - SCOPUS:84857283572

SN - 0002-9939

VL - 140

SP - 1947

EP - 1956

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -

Homeomorphisms between limbs of the Mandelbrot set

Abstract

Access to Document

Other files and links

Fingerprint

Cite this