iteration of fractional linear functions

[tommy1729]

Unfortunately someone else was already faster. There is a very recent (May 2009) Chinese article:
Shi, YongGuo; Chen, Li: Meromorphic iterative roots of linear fractional functions,Science in China Series A: Mathematics Vol 52 Iss 5, p. 941-948
If you are interested, download quickly; I dont know how long this link will be available for free.

well actually many such papers are written regularly.

also for free ; i remember han de bruijn posting one on sci.math.

i " wrote " about some too , however " wrote " is literal : on paper

in your pdf , you find an answer to a question , you asked me recently.

more particular , i said polynomials of degree 2 have no iterate root from C to C.

you asked " why " and " are you sure "

well ref 12 in the pdf is why

i quote from the first (!) page , the introduction (!) :

" Concerning polynomial functions, the result of [12] implies that quadratic polynomial functions have no n-th (n >= 2) iterative root from C to itself. Similar results concerning some other polynomials can be found in [13]. "

which thus confirms what i said , already in the introduction.


high regards

tommy1729

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actually i use ordinary algebra for this ...
...
for half - iterate , just ordinary algebra.

Well then demonstrate.

simple.

just use f(x) = a' x + b' / c' x + d'

and expand f(f(x))

now set f(f(x)) equal to your a x + b / c x + d

and solve for a' b' c' and d'

then f(x) is your half-iterate by ordinary algebra.

trivial.


regards

tommy1729