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 Bivariate quasi-holomorphic function T(x,y) for complex x and y bo198214 Administrator Posts: 1,395 Threads: 91 Joined: Aug 2007 09/07/2010, 03:58 PM (This post was last modified: 09/07/2010, 04:01 PM by bo198214.) Hey Ciera, welcome on board, before my retreat, some points about your post: I tried a bit about this "boundedness criterion" whether quasi-holomorphic or only holomorphic in the second variable. However I couldnt find a uniqueness criterion (for general functions not only exponentiation though). Such a criterion would be of great value, because it would unite the case be^(1/e) because it is applicable for both. I can give you only the two references containing uniqueness criterion for the case with real fixed point: http://citeseerx.ist.psu.edu/viewdoc/sum...1.154.3249 and the case of two complex fixed points: http://arxiv.org/abs/1006.3981 also Mike3 posted lately a nice uniqueness criterion for regular iteration at a real fixed point. I am not sure whether considering the bivariate holomorphism really helps for uniqueness. But I wish you luck in proving such a criterion, really! (Dont forget however to make sure that your uniqueness criterion can be satisfied by any function at all!) « Next Oldest | Next Newest »

 Messages In This Thread Bivariate quasi-holomorphic function T(x,y) for complex x and y - by Ciera_ΩMega - 09/04/2010, 05:25 PM RE: Bivariate quasi-holomorphic function T(x,y) for complex x and y - by bo198214 - 09/07/2010, 03:58 PM RE: Bivariate quasi-holomorphic function T(x,y) for complex x and y - by tommy1729 - 09/07/2010, 07:50 PM RE: Bivariate quasi-holomorphic function T(x,y) for complex x and y - by bo198214 - 09/08/2010, 02:23 AM RE: Bivariate quasi-holomorphic function T(x,y) for complex x and y - by mike3 - 09/08/2010, 05:20 AM

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