Is sexp(z) pseudounivalent for Re(z) > 0 ? - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)+--- 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 |