Skip to main content
×
Home
    • Aa
    • Aa

Julia sets of uniformly quasiregular mappings are uniformly perfect

  • ALASTAIR N. FLETCHER (a1) and DANIEL A. NICKS (a2)
Abstract
Abstract

It is well known that the Julia set J(f) of a rational map f: is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus, with the bound depending only on f. In this paper we prove that an analogous result is true in higher dimensions; namely, that the Julia set J(f) of a uniformly quasiregular mapping f: nn is uniformly perfect. In particular, this implies that the Julia set of a uniformly quasiregular mapping has positive Hausdorff dimension.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[6]L. Carleson and T. Gamelin Complex Dynamics (Springer-Verlag, 1993).

[18]S. Rickman Quasiregular mappings. (Springer-Verlag1993).

[23]M. Vuorinen Conformal Geometry and Quasiregular Mappings. (Springer-Verlag, 1988).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×