  Core structures of a single vortex in A-like and B-like phases of superfluid
3He in uniaxially compressed and stretched aerogels are studied by numerically
solving Ginzburg-Landau equations derived microscopically. It is found that,
although the A-like phase with axial pairing is extended by any uniaxial
deformation, the vortex core states in the two phases depend highly on the type
of deformation in aerogel: In a compressed aerogel, the first order vortex core
transition (VCT) previously seen in the bulk B phase appears at any pressure in
B-like phase, while no strange vortex core is expected in A-like phase. By
contrast, in a stretched aerogel, the VCT in B-like phase is lost, while
another VCT is expected to occur between a nonunitary core and the polar one in
A-like phase. An experimental search for these results is hoped to understand
correlation between superfluid $^3$He and aerogel structures.
