We show that percolation and structural arrest transitions coexist in diffe
rent regions of the phase diagram of a copolymer-micellar system and relate
them to short-range intermicellar attraction. The intermediate scattering
function shows a nonergodic transition along a temperature and concentratio
n dependent line. Analyses show a logarithmic time dependence, attributed t
o a higher-order glass transition singularity predicted by mode-coupling th
eory, followed by a power law.