Homeomorphisms of the Mandelbrot Set
| dc.creator | Jung, Wolf | |
| dc.date | 2003-12-14 | |
| dc.date.accessioned | 2026-07-07T06:26:51Z | |
| dc.date.available | 2026-07-07T06:26:51Z | |
| dc.description | On subsets E of the Mandelbrot set 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: E to E in the parameter plane. Each h has two fixed points in E, and a countable family of mutually homeomorphic fundamental domains. Possible generalizations to other families of polynomials or rational mappings are discussed. The homeomorphisms on subsets E of M constructed by surgery are extended to homeomorphisms of M, and employed to study groups of non-trivial homeomorphisms h: M to M . It is shown that these groups have the cardinality of the continuum, and they are not compact. | |
| dc.description | Preprint of a paper submitted to Dynamics in the Complex Plane, proceedings of a symposium in honour of Bodil Branner, June 19--21 2003, Holbaek | |
| dc.identifier | https://arxiv.org/abs/math/0312279 | |
| dc.identifier | http://arxiv.org/abs/math/0312279 | |
| dc.identifier | Dynamics on the Riemann Sphere, A Bodil Branner Festschrift, P. G. Hjorth, C. L. Petersen Eds., EMS January 2006, pp 139-159. ISBN 3-03719-011-6. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97238 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F45 | |
| dc.title | Homeomorphisms of the Mandelbrot Set | |
| dc.type | text |