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 regular sexp:different fixpoints sheldonison Long Time Fellow Posts: 648 Threads: 22 Joined: Oct 2008 08/08/2009, 04:15 AM (This post was last modified: 08/08/2009, 04:22 AM by sheldonison.) (08/06/2009, 08:56 PM)Gottfried Wrote: When I was reading Dmitrie's & Henryk's (newest(?)) paper on superfunctions I tried to get an own impression about the differences of tetration when regular iteration is applied with different fixpoints. (see picture 4 at page 22) .... There are two aspects which make me headscratching. (1) I could naively easier accept, if one of the functions proceeds faster and the other one slower; maybe with some modification, for instance a turning point at the center or something like that. But we have permanently changing signs - contradicting the assumtion of a somehow smoothely increasing function. But ok, the behave of the difference can be caused by one of the involved, say by the high (repelling)-fixpoint-version tet4. (2) But this seems also not to hold. If I assume that at least the tet2-function is smoothely increasing, then a first guess may be, that all differences of all orders should have monotonuous behave. But that's also not true: looking at differences of high order (>24) we find sinusoidal behave in the magnitude of <1e-24. Consequence: very likely also the tet2-function, although based on the attracting fixpoint, has a sinusoidal component in that interval 2

 Messages In This Thread regular sexp:different fixpoints - by Gottfried - 08/06/2009, 08:56 PM RE: regular sexp:different fixpoints - by sheldonison - 08/08/2009, 04:15 AM RE: regular sexp:different fixpoints - by Gottfried - 08/11/2009, 03:19 PM RE: regular sexp:different fixpoints - by bo198214 - 08/11/2009, 03:42 PM RE: regular sexp:different fixpoints - by Gottfried - 08/11/2009, 03:52 PM RE: regular sexp:different fixpoints - by bo198214 - 08/11/2009, 04:12 PM RE: regular sexp:different fixpoints - by jaydfox - 08/11/2009, 06:47 PM

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