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This paper, the third in a series, completes our description of all (radial)solutions on C* of the tt*-Toda equations, using a combination of methods fromp.d.e., isomonodromic deformations (Riemann-Hilbert method), and loop groups.We place these global solutions into the broader context of solutions which aresmooth near 0. For such solutions, we compute explicitly the Stokes data andconnection matrix of the associated meromorphic system, in the resonant casesas well as the non-resonant case. This allows us to give a complete picture ofthe monodromy data of the global solutions.

Isomonodromy aspects of the tt* equations of Cecotti and Vafa III. Iwasawa factorization and asymptotics