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+--- Thread: Is sexp(z) pseudounivalent for Re(z) > 0 ? (/showthread.php?tid=844)
Is sexp(z) pseudounivalent for Re(z) > 0 ? - tommy1729 - 03/25/2014
Is sexp(z) pseudounivalent for Re(z) > 0 ?
Is that a uniqueness condition ?
The difference between univalent and pseudounivalent is :
speudounivalent is weaker : f(z+k) = f(z) only possible if k is real.
regards
tommy1729
RE: Is sexp(z) pseudounivalent for Re(z) > 0 ? - tommy1729 - 03/25/2014
I have to add : psuedounivalent must be a uniqueness criterion but without existance proven.
This follows from the earlier proven fact that sexp(z) analytic for Re(z)>0 is already a uniqueness criterion.
Hence the question becomes : is this analytic function sexp(z) pseudounivalent ?
We know that sexp(z) has singularies. In the thread " the fermat superfunction " I noticed that most entire functions are not pseudounivalent. The follows from the nonbijective nature of most entire functions and the many amount of fixpoints/zero's of most entire functions.
This motivated me to wonder about functions that are not entire hence returning to sexp(z).
Naturally I also wonder about other superfunctions ofcourse.
I do not recall the exact location of all previous posts regarding these issues but on MSE mick made a related post.
The case which mick answer is actually about exp, but the same applies by analogue to sexp for Re(z)>0.
http://math.stackexchange.com/questions/192905/boundedness-on-strips-in-the-complex-plane-for-functional-equations
Btw his score of -5 is rediculous.
This reminds me of the reasons why I am not or no longer on places such as MSE , sci.math, wiki etc.
Tetration forum rules
But other tend not too imho.
regards
tommy1729
RE: Is sexp(z) pseudounivalent for Re(z) > 0 ? - tommy1729 - 03/26/2014
Let a,b > 0. Let a',b' > 0.
Because exponential iterations of a + b i usually get arbitrarily close to any other a' + b' i , I am tempted to say that sexp(z) is NOT psuedounivalent.
So entire superfunctions are usually not pseudounivalent and since many iterations of analytic functions behave chaotic (like exp) , neither are most nonentire superfunctions.
So, what is an example of a nontrivial pseudounivalent superfunction ?
If they exist at all ?
Together with my friend mick im working on this.
Im pessimistic though.
And you ?
regards
tommy1729
RE: Is sexp(z) pseudounivalent for Re(z) > 0 ? - tommy1729 - 03/26/2014
Related : http://math.eretrandre.org/tetrationforum/showthread.php?tid=490&pid=6839#pid6839
SO probably no twice a superfunction.
regards
tommy1729