Recent content by goosefrabbas

Homework Statement How many points in ΣN are fixed by σkN? Homework Equations σkN is the kth iteration of the shift map σN. The Attempt at a Solution I'm not sure where to start. I probably just need a hint.

I changed my interval I to (-.5, .5) so that part 2 would work. And for part 3, I got this far. Fλ(x)=λ(x3-x) is an odd function, so the second iteration of Fλ(x0) = x0. Using algebra I got x = (1 +- sqrt(1 - 4λ))/(2λ), so this is the 2-cycle for Fλ, but only for 0<λ<1/4. For part 4, As λ ->...

Homework Statement Consider the families of iterating functions Fλ(x) = λ(x3 - x). Fλ(x) undergoes a bifurcation at λ=1, about the fixed point x=0. Figure out what ilk of bifurcation is occurring for Fλ(x) and prove your assertion rigorously.Homework Equations My book says this about...