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The dynamics of galactic systems with central binary black holes is studied.The model is a modification from the restricted three body problem, in which agalactic potential is added as an external potential. Considering the case withan equal mass binary black holes, the conditions of existence of equilibriumpoints, including Lagrange Points and additional new equilibrium points, i.e.Jiang-Yeh Points, are investigated. A critical mass is discovered to befundamentally important. That is, Jiang-Yeh Points exist if and only if thegalactic mass is larger than the critical mass. The stability analysis isperformed for all equilibrium points. The results that Jiang-Yeh Points areunstable could lead to the core formation in the centers of galaxies.

Galaxies with Supermassive Binary Black Holes: (I) A Possible Model for the Centers of Core Galaxies