## Renormalization of wave function fluctuations for a generalized Harper equation

A renormalization analysis is presented for a generalized Harper equation

(1 + Î± cos(2Ï€(Ï‰(i + 1/2) + Ï†)))Ïˆi+1 + (1 + Î± cos(2Ï€(Ï‰(i âˆ’ 1/2) + Ï†)))Ïˆiâˆ’1

+2Î» cos(2Ï€(iÏ‰ + Ï†))Ïˆi = EÏˆi. (0.1)

For values of the parameter Ï‰ having periodic continued-fraction expansion,

we construct the periodic orbits of the renormalization strange sets in function

space that govern the wave function fluctuations of the solutions of the

generalized Harper equation in the strong-coupling limit Î»â†’âˆž.

For values of Ï‰ with non-periodic continued fraction expansions, we make

some conjectures based on work of Mestel and Osbaldestin on the likely

structure of the renormalization strange set.

http://dspace.stir.ac.uk/bitstream/1893/208/1/thesis_23may07_new.pdf