Solving tetration for base 0 < b

Linear Mode

Solving tetration for base 0 < b < e^-e

bo198214 Offline

Administrator

Posts: 1,631
Threads: 107
Joined: Aug 2007

09/12/2009, 07:20 AM

(09/12/2009, 06:56 AM)bo198214 Wrote: So I would consider the regular iteration of \( g(x)=f^{\circ 2}(x)=b^{b^x} \) and then just always take the half of the iteration number \( f^{\circ t}(x)=g^{\circ t/2}(x) \).

The interesting thing is that \( g \) not only has the two attracting fixed points \( p_1 \) and \( p_2 \) but also a repelling fixed point in between. Which is attractive for \( g^{-1} \) in the range \( (p_1,p_2) \).

Graph for b=0.01 with p1=0.941482102273016 and p2=0.0130925205079953.

So why not do regular iteration at that inbetween fixed point?

Website Find

« Next Oldest | Next Newest »

Messages In This Thread

Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 02:00 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 06:56 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:20 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 07:40 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:47 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:07 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 08:35 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:50 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 03:48 PM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 09:04 PM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 06:14 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 07:24 AM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 09:57 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 11:23 AM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 11:44 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/14/2009, 09:43 PM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/17/2009, 08:01 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/17/2009, 11:03 AM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 01:34 PM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 07:34 PM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/14/2009, 02:02 PM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 08:08 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 09:49 AM

RE: Solving tetration for base 0 < b < e^-e - by tommy1729 - 09/18/2009, 12:16 PM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/18/2009, 01:00 PM

Possibly Related Threads…
Thread		Author	Replies	Views	Last Post
	[2sinh] exp(x) - exp( - (e-1) x), Low Base Constant (LBC) 1.5056377..	tommy1729	3	5,911	04/30/2023, 01:22 AM Last Post: tommy1729
	Base -1	marraco	15	37,463	07/06/2022, 09:37 AM Last Post: Catullus
	I thought I'd take a crack at base = 1/2	JmsNxn	9	13,584	06/20/2022, 08:28 AM Last Post: Catullus
	solving f(g(x)) = f(x) converging to f(exp(x)) = f(x)	tommy1729	2	4,378	05/26/2022, 11:07 PM Last Post: JmsNxn
	Repetition of the last digits of a tetration of generic base	Luknik	12	19,834	12/16/2021, 12:26 AM Last Post: marcokrt
	On the [tex]2 \pi i[/tex]-periodic solution to tetration, base e	JmsNxn	0	3,533	09/28/2021, 05:44 AM Last Post: JmsNxn
	A different approach to the base-change method	JmsNxn	0	3,915	03/17/2021, 11:15 PM Last Post: JmsNxn
	Complex Tetration, to base exp(1/e)	Ember Edison	7	23,419	08/14/2019, 09:15 AM Last Post: sheldonison
	b^b^x with base 0<b<e^-e have three real fixpoints	Gottfried	1	9,442	11/07/2017, 11:06 AM Last Post: sheldonison
	Analytic matrices and the base units	Xorter	2	10,384	07/19/2017, 10:34 AM Last Post: Xorter

View a Printable Version

Users browsing this thread: 2 Guest(s)

Login
Username:
Password:	Lost Password?
	Remember me