Wolf Jung
Published 2003-12-14Version 1
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.
Comments: 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
Journal: 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.
Multipliers of periodic orbits of quadratic polynomials and the parameter plane
Topological entropy of quadratic polynomials and dimension of sections of the Mandelbrot set
New Approximations for the Area of the Mandelbrot Set
![QR code for arXiv:math/0312279 [math.DS]](http://oss.arxitics.com/images/favicon.svg)