A conjugacy problem

mark
Tue, 19 Sep 2017 13:18:40 +0000
Quiz or Test Prep

Let [imath]f(x) = x^2 + 1/4[/imath], let [imath]g(x) = x^2+2 x+1/4[/imath], and let [imath]\varphi(x) = x+1[/imath].

Show that [imath]\varphi[/imath] conjugates [imath]f[/imath] to [imath]g[/imath], i.e. [imath]f\circ \varphi = \varphi \circ g[/imath]

Suppose I tell you that [imath]f[/imath] has a neutral fixed point at [imath]x=1/2[/imath]. How can you use this information to find a neutral fixed point for [imath]g[/imath]?