WKB-analysis of Hitchin system in the Garnier case with 5 punctures

After a brief account of tame non-abelian Hodge theory and Riemann--Hilbert correspondence, we turn to the study of the large scale behavior of these maps, given in my preprint arXiv:2103.00932.
Their description is reminiscent of classical results in BKW analysis, and relies on a number of recent results : asymptotic models of solutions of Hitchin's equations given by T. Mochizuki and
R. Mazzeo et al, and explicit co-ordinates in the spirit of Teichmueller theory on the character variety introduced by C. Simpson.