Let $M$ be a smooth manifold. A fixed point $x$ of a diffeomorphism $f\colon M\to M$ is said to be a hyperbolic fixed point if $Df(x)$ is a linear hyperbolic isomorphism. If $x$ is a periodic point of least period $n$ it is called a hyperbolic periodic point if it is a hyperbolic fixed point of $f^n$ (the $n$ th iterate of $f$ .

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.