1,362 reputation
213
bio website
location Austin, TX
age 52
visits member for 1 years, 6 months
seen 5 hours ago

I'm interested in tetration, and complex dynamics and iteration theory. I'm seeking to learn more about math, so I can prove some of the things I've posted on some other forums.


Apr
16
comment radius of convergence of half iterate of sinh(z)?
@GottfriedHelms, I am deleting my earlier comments; disregard my image; your update looks great. The only thing I would add, is that this image is the Leau-Fatou flower. There are two slightly different analytic versions of the continuous Leau-Fatou flower generated via $\alpha^{-1}(\alpha(z_0)+n)$, where n varies from $\pm \infty$, depending on which quadrant the $\alpha(z)$ Abel function is generated from.
Apr
16
suggested suggested edit on radius of convergence of half iterate of sinh(z)?
Apr
15
awarded  Self-Learner
Apr
15
comment radius of convergence of half iterate of sinh(z)?
@MarkMcClure Is there any four-petal case where the half iterate, generated from either petal, would be the same? I guess I can save that question for some future time ....
Apr
15
comment radius of convergence of half iterate of sinh(z)?
Thanks Gottfried. The theory of parabolic fixed points is pretty cool. It is also the gateway to the parabolic implosion, and Quasi-conformal maps; most of which is still over my head!
Apr
15
revised radius of convergence of half iterate of sinh(z)?
typo, swapped results
Apr
15
comment radius of convergence of half iterate of sinh(z)?
ah, it appears the two results are swapped! doesn't surprise me.... :) I fixed it.
Apr
13
comment Does the Mandelbrot fractal contain countably or uncountably many copies of itself?
Also, see this mathstack question; math.stackexchange.com/questions/491279/mandelbrot-boundary/… Each Period n component has a period "n" attracting fixed point. If the fixed point is zero (at the center), it is super-attracting. The boundary of the component is where the fixed point changes from attracting to neutral, or parabolic.
Apr
13
comment Does the Mandelbrot fractal contain countably or uncountably many copies of itself?
Converse is true. see: Complex Dynamics by Lennart Carleson, Chapter 8.1, Quadratic polynomials, the Mandelbrot set. Super attracting points have derivative of zero. These are centers of repeating components, $f^n=f^0$, where the derivative is zero. Turns out all bulbs/cardioids have such a center point where the derivative is zero, which means that center is asolution of f^n(0)=0.
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
clarity
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
equations to show what the next step I took was
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
equations to show what the next step I took was
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
added 123 characters in body
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
deleted 133 characters in body
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
added 132 characters in body
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
deleted 1 characters in body
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
deleted 30 characters in body
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
added 94 characters in body
Apr
10
revised Show that the iterated $\ln^{[n]}$ of tetration(x,n) is nowhere analytic
added 581 characters in body
Apr
10
revised Relationship between the Weierstrass function and other fractals
spelling reciprocal