Planet-planet scattering occurs when planets in orbit around a star are spaced closely enough that gravitational interactions lead to crossing orbits, collisions, and ejections of some of the planets. This scenario is successful at reproducing the observed eccentricity distribution of exoplanets. When this scattering takes place around a single star, ejected planets are free to directly leave the system. In a binary star system, escape is complicated somewhat by the presence of the binary companion; depending on the energy with which a planet is ejected, its only allowed escape route may lie through the space surrounding the secondary. An escaping planet can find itself transiently orbiting the star it was not born around, or `bouncing’ back and forth between the two stars. This is the focus of Moeckel & Veras 2012,"Exoplanets Bouncing Between Binary Stars".
These animations show some examples of this phenomenon. In this binary, the primary star has three planets and the other star has one. The left panel shows the system in an inertial frame. The right panel is in a frame rotating with the binary, so that the stars are fixed. Here space is divided into allowed (beige) and disallowed (red) regions, depending on the instantaneous dimensionless energy of the escaping planet, shown as the Jacobi constant C. Changes to the topology of the allowed space are achieved via further interactions with the planets around the planet-hosting star. Escape from the binary is impossible until these interactions change the Jacobi constant such that the inner allowed region is connected to the outer allowed region.
Capture of the planet by the other star is not possible without some dissipative force to change the Jacobi constant of a bouncing planet. One way to supply an extra force is by interactions with more bodies around the secondary. In this final example, a single planet is orbiting the secondary. After the planet is launched from its host star, interactions with the planet around the other star change its Jacobi constant such that it can no longer transfer back to its host. Several Myr after this movie ends, the planet originally around the blue star is ejected, having been displaced by the bouncing planet.