Solutions of Doubly and Higher Order Iterated Equations |
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| Authors: | Becky A Brown A Ray Brown Michael F Shlesinger |
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| Institution: | (1) Naval Research Laboratory, 4555 Overlook Avenue, SW Washington, District of Columbia, 20375;(2) 4650 N. Washington Blvd., Arlington, Virginia, 22201;(3) Office of Naval Research, 800 Quincy Avenue Arlington, Virginia, 22210 |
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| Abstract: | Michael Fisher once studied the solution of the equation f(f(x))=x
2–2. We offer solutions to the general equation f(f(x))=h(x) in the form f(x)=g(ag
–1(x)) where a is in general a complex number. This leads to solving duplication formulas for g(x). For the case h(x)=x
2–2, the solution is readily found, while the h(x)=x
2+2 case is challenging. The solution to these types of equations can be related to differential equations. |
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| Keywords: | Dynamical systems iterated equations duplication equations finite difference equations |
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