  The concept of sliding Shilnikov connection has been recently introduced and
represents an important entity of Filippov systems because its existence
implies chaotic behavior on an invariant subset of the system. The
investigation of its properties have just begun, and understanding the topology
and complexity of its invariant set is of primordial interest. In this paper,
we conduct a local analysis on the first return map associated to a Shilnikov
sliding connection, which reveals an infinite iterated function system
structure satisfying the so-called conformal conditions. By using the theory of
conformal iterated function systems, we estimate the Hausdorff dimension of the
invariant set of the first return map, showing, in particular, that it is
positive and less than 1. Moreover, we provide that such an invariant set,
adjoined with the regular-fold point, is actually a Cantor set.
