mdbtxt1
mdbtxt2
Proceed to Safety

Hyperbolic Component    

Robert P. Munafo, 2023 Jun 21.



Name used by many mathematicians in earlier papers to refer to a mu-atom. It appears to have originated with John Milnor, in notes that were first published in this 1992 paper but the term was in use some years earlier.

We consider polynomial maps f : C → C of degree d ≥ 2 , [...] the hyperbolic maps in CS form an open set HS called the hyperbolic connectedness locus. The various connected components Hα ⊂ HS are called hyperbolic components [...]

This is a more general name for any region in any parameter plane whose members have iteration dynamics with hyperbolic properties.


revisions: 20020506 oldest on record; 20230621 quote and bibliography link




From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

Mu-ency main pageindexrecent changesDEMZ


Robert Munafo's home pages on AWS    © 1996-2024 Robert P. Munafo.    about    contact
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Details here.

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2023 Jun 22. s.27