Let be a smooth manifold. A fixed point of a diffeomorphism is said to be a hyperbolic fixed point if is a linear hyperbolic isomorphism. If is a periodic point of least period , it is called a hyperbolic periodic point if it is a hyperbolic fixed point of (the -th iterate of ).

If the dimension of the stable manifold of a fixed point is zero, the point is called a source; if the dimension of its unstable manifold is zero, it is called a sink; and if both the stable and unstable manifold have nonzero dimension, it is called a saddle.