We introduce a Basmajian-type series identity on holomorphic families of limit sets associated to familiar one-dimensional complex dynamical systems. We show that the series is absolutely convergent if and only if the Hausdorff dimension of the limit set is strictly less than one. In particular, this allows us to extend the Basmajian identity to certain Schottky groups and to find the Hausdorff dimension one locus in the complement of the Mandelbrot set for quadratic polynomials. Speaker(s): Yan Mary He (UChicago)