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We introduce a way of presentation of pairs $(E,\nabla)$, where $E$ is abundle on a Riemann surface and $\nabla$ is a logarithmic connection in $E$,which is based on a presentation of the surface as a factor of the exterior ofthe unit disc. In this presentation we write the local equation ofisomonodormic deformation of pairs $(E,\nabla)$. These conditions are writtenas a modified Schlesinger system on a Riemann sphere (and in the typical casejust as an ordinary Schlesinger system) plus some linear system.

The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces