The Curse of the Black Spot by a Siren-like creature who marks people with black spots on their palms after they are injured and appears to disintegrate them with her touch after putting them in a trance. Rory Williams receives a cut during a tussle with the pirates, and finds a black spot on his hand, but is prevented from succumbing to the song of the Siren by Amy Pond and the Doctor. Surmising the Siren is using water as a portal, the Doctor instructs the crew to seek refuge in the ship's dry magazine. There, they find Toby Avery, the son of the ship's captain
Dynamical billiards Dynamical billiards A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed. Billiard dynamical systems are Hamiltonian idealizations of the game of billiards, but where the region contained by the boundary can have shapes other than rectangular and even be multidimensional. Dynamical billiards may also be studied on non-Euclidean geometries; indeed, the very first studies of billiards established their ergodic motion on surfaces of constant negative curvature. The study of billiards which are