### Definition of parabolic Julia sets

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#### marcm200

• Fractal Frogurt
• Posts: 491

#### Definition of parabolic Julia sets

« on: May 07, 2019, 03:25:47 PM »
I'm sure this is one of the most basic questions - I searched for some time (obviously in the wrong places), but could not find an answer.

How exactly is the term "parabolic" (and hyperbolic) Julia set defined? The only thing I did find, was, that parabolic Julia sets show slow dynamics.

EDIT: 10. August 2019: I removed the question prefix as it is answered below.

« Last Edit: August 10, 2019, 03:55:35 PM by marcm200, Reason: Removed "question" prefix »

• Fractal Feline
• Posts: 195

#### Re: Definition of parabolic Julia sets

« Reply #1 on: May 07, 2019, 06:32:00 PM »

#### marcm200

• Fractal Frogurt
• Posts: 491

#### Re: Definition of parabolic Julia sets

« Reply #2 on: May 08, 2019, 08:14:36 AM »
Thanks, that helped, especially your definition. Now I know where to look next (multiplier, what a strange name...)

#### marcm200

• Fractal Frogurt
• Posts: 491

#### Re: Definition of parabolic Julia sets

« Reply #3 on: August 10, 2019, 03:54:04 PM »
I was computing some Julia sets for z^n+A*z+c (n=2,3,4 or 5) and judged the fix points when I noticed a parabolic one never comes together with an attracting fix point. Does this not happen at all? Or is it just the region I am looking in (A, c are either pure real or imaginary in the 2-square).

Does a parabolic period-2-cycle exist?

Can there be two or more parabolic fix points in one Julia set as for the repelling and attracting ones is possible?

EDIT: 10. August 2019: I removed the "question" prefix as it is answered.

EDUT: 25 September 2019: continued here: https://fractalforums.org/fractal-mathematics-and-new-theories/28/parabolic-julia-sets/3091/msg16906#new

« Last Edit: September 25, 2019, 09:07:27 AM by marcm200, Reason: continues in more appropriate sub-forum »

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