We present a new symplectic algorithm that has the desirable properties of the sophisticated but highly efficient numerical algorithms known as mixed variable symplectic (MVS) methods and that, in… Expand

The discovery by Marcy and coworkers of two planets in 2 : 1 orbital resonance about the star GJ 876 has been supplemented by a dynamical fit to the data by Laughlin & Chambers, which places the… Expand

We consider the dynamical evolution of bound, hierarchical triples of supermassive black holes that might be formed in the nuclei of galaxies undergoing sequential mergers. The tidal force of the… Expand

We investigate the dynamical evolution of coplanar, hierarchical, two-planet systems where the ratio of the orbital semimajor axes α = a1/a2 is small. Hierarchical two-planet systems are likely to be… Expand

The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In… Expand

Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly… Expand