# Quadratic Maps Two-Cycles

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Show that the 2-cycle of the quadratic map is stable if 3/4<5/4. The quadratic map is x(n+1)=x(n)^2-c.

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The expert shows that the two-cycle of a quadratic map is stable if 3.4<5/4. The quadratic map functions are provided.

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Show that the 2-cycle of the quadratic map is stable if ¾ < c < 5/4. The quadratic map is x = x - c.

Solution: A 2-cycle exists if and only if there are two points and such that and . Equivalently, such a must satisfy , where . Hence is a fixed point of the ...

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