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 Cyclic dynamics f(-x) = T (f(x)) tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 08/24/2015, 11:56 PM Let analytic a(z) = a^[r](z) for all z and some real r <> 1. Cyclic dynamics fundamental equation. F( a(z) ) = T ( F(z) ) With T entire. Less general By using g(q x) = a( g(x) ) , q = exp(2 pi i / r). We get W(q x) = T( W(x) ). --- Example F(-x) = F(x) + pi i Solution ln(x). Can you find F(-x) = g * F(x) + h Note 1) we consider only nonconstant solutions Note 2) we prefer a(x) to have exactly one fixpoint , so that its iterations are Unique ! Regards Tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Cyclic dynamics f(-x) = T (f(x)) - by tommy1729 - 08/24/2015, 11:56 PM RE: Cyclic dynamics f(-x) = T (f(x)) - by tommy1729 - 08/25/2015, 08:13 AM RE: Cyclic dynamics f(-x) = T (f(x)) - by tommy1729 - 08/25/2015, 08:23 AM

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