Extensions of homeomorphisms between limbs of the Mandelbrot set
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- by Bodil Branner and Núria Fagella PDF
- Conform. Geom. Dyn. 5 (2001), 100-139 Request permission
Abstract:
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), 327–390) which proves – without assuming local connectivity of the Mandelbrot set – that these maps are compatible with the embedding of the limbs in the plane. Outside the limbs, the constructed extension is quasi-conformal.References
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Additional Information
- Bodil Branner
- Affiliation: Department of Mathematics, Technical University of Denmark, Building 303, DK-2800 Kongens Lyngby, Denmark
- Email: B.Branner@mat.dtu.dk
- Núria Fagella
- Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
- Email: fagella@maia.ub.es
- Received by editor(s): September 4, 2000
- Received by editor(s) in revised form: May 10, 2001
- Published electronically: October 18, 2001
- Additional Notes: Partially supported by SNF Grant No. 9701387
Partially supported by DGICYT Grant No. PB96-1153, BFM2000-0805-C02-01 and CIRIT 2000SGR-27 - © Copyright 2001 American Mathematical Society
- Journal: Conform. Geom. Dyn. 5 (2001), 100-139
- MSC (2000): Primary 37F45; Secondary 37F10
- DOI: https://doi.org/10.1090/S1088-4173-01-00069-8
- MathSciNet review: 1872159