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how many zero's ? - tommy1729 - 05/09/2012
Hi When trying to glue some ideas together i often stumble upon the problem of finding zero's / fixpoints and the amount of zero's / fixpoints. Not just the computation , but the proof for such a problem with real parameters. Despite the existence of complex analysis tools such as the argument principle , fractals , lagrange multipliers and riemann surfaces the problem still seems " hard " in the general case. Maybe it requires just a lot of work and educated guesses and the use of rouchÃ© theorem but i would like a more systematic approach. A good example of what i mean is this: Let the amount of distinct complex zero's in terms of the real parameters a,b,c be written as N(a,b,c). Express N(a,b,c) for the function f(z) - z := 2*sinh(a*z*(1+exp(b*z^2 + c*z^4))) - z How to deal with that ? Maybe consider abs ( f ' (z) ) = 1 ? regards tommy1729 |