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 some questions about sexp tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 06/28/2010, 11:18 PM im going to ask some questions about sexp , and i mean all proposed solutions of sexp. (question 1) does the following hold : d f^n / d x^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k ? (question 2) since slog(z) (base e) has period 2pi i why doesnt sexp(z) look like a log spiral ? or does it , like having a branch cut at real x < -2 ? (question 3) what happens to limit cycles and n-ary fixpoints ?? sure we can set the fixpoints exp(L) = L at oo i but how about the fixpoints of exp(exp(.. q)) = q and limit cycles of the exp iterations ... e.g. let e^q1 = q2 , e^q2 = q1 , if we want half-iterates , 1/3 iterates and sqrt(2) iterates to have the same fixpoints , this is a problem , not ? perhaps we can 'hide' L at +/- oo i ( like kouznetsov ) and 'hide' the other points at - oo ?? (question 4) do all 'analytic in the neigbourhood of the positive reals' sexp have the fixpoints exp(L) = L at oo i ? ( i know that [L,sexp(slog(L)+o(1))] cannot be in the analytic zone , but maybe [L,sexp(slog(L)+o(1))] isnt part of the analytic zone ) (question 5) slog(z) base x is not holomorphic in x in a domain containing the interval [a,b] if eta is between a and b. why is that ? i know that the real fixpoint dissappears but still ... sorry if those are FAQ or trivial Q. regards tommy1729 « Next Oldest | Next Newest »