Spiral waves are investigated in chemical systems whose underlying spa
tially homogeneous dynamics is governed by a deterministic chaotic att
ractor. We show how the local periodic behavior in the vicinity of a s
piral defect is transformed to chaotic dynamics far from the defect. T
he transformation occurs by a type of period doubling as the distance
from the defect increases. The change in character of the dynamics is
described in terms of the phase space flow on closed curves surroundin
g the defect.