2D Iterations

John H. Hubbard and Beverly H. West
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John H. Hubbard: Cornell University, Department of Mathematics
Beverly H. West: Cornell University, Department of Mathematics

Chapter 13 in MacMath 9.0, 1992, pp 87-94 from Springer

Abstract: Abstract For a system of two equations of the form: $$\text{y}=\text{f}(\text{x,y}),\;\;\;\;\text{y}=\text{g}(\text{x,y})$$ and a given seed or initial point (x 0, y 0), this program plots the orbit under iteration. That is, it plots the sequence of points (x 0, y 0), (x 1, y 1), (x 2, y 2), (x 3, y 3),…, where $$\begin{matrix}x_1 = & f(x_0) \\ x_2 = & f(x_1) = & f(f(x_0)) = & f^{\circ 2}(x_0) \\ x_3 = & f(x_2) = & f(f(f(x_0))) = & f^{\circ 3}(x_0). \\ \vdots \end{matrix}$$

Keywords: Periodic Point; Rotation Number; Siegel Disk; Walk Away; Henon Mapping (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-1-4684-0390-9_13

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