Let H be a diffeomorphism and let f be a vector field, respectively,
possessing a hyperbolic fixed point p. The λ-lemma says that a transversal
section of stable manifold $W^s_{loc}(p)$ converges under the flow to the
unstable manifold $W^u_{loc}(p)$ with exponential rate. The strong λ-Lemma
makes an analogous statement for transversal sections of an extended stable
manifold. Those sections converge under the flow exponentially fast to the
strong unstable manifold. In a paper by B.Deng, J. Differ. Equations 79,
No. 2, 189-231 (1989), these statements have been proved within the vector
field context, applying analysis used for solving the Sil'nikov-problem. In
the present bachelor thesis, we present these proofs in full detail.
Furthermore, we carry the proof of the λ-lemma over to the discrete
setting.