  We report on and analyze the textural transformations in islands, thicker
circular domains, floating in very thin free standing chiral Smectic C* liquid
crystal films. As an island is growing, an initial pure bend texture of the
c-director changes into a reversing spiral at a critical size. Another distinct
spiral texture is induced by changing the boundary condition at the central
point defect in the island. To understand these transformations from a pure
bend island, a linear stability analysis of the c-director free energy is
developed, which predicts a state diagram for the island. Our observations are
consistent with the theoretical phase diagram.
