Abstract
Using an analogy of the Lattès’ construction of chaotic rational functions, we show that there are uniformly quasiregular mappings of the n n -sphere R ¯ n \overline {{\Bbb R}}^n whose Julia set is the whole sphere. Moreover there are analogues of power mappings, uniformly quasiregular mappings whose Julia set is S n − 1 {\Bbb S}^{n-1} and its complement in S n {\Bbb S}^{n} consists of two superattracting basins. In the chaotic case we study the invariant conformal structures and show that Lattès type rational mappings are either rigid or form a 1-parameter family of quasiconformal deformations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Conformal Geometry and Dynamics of the American Mathematical Society
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
