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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.

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