Generating maps, invariant manifolds, conjugacy

The idea of generating functions and maps is presented, first in global symplectic geometry and then in the theory of invariant manifolds, as introduced by McGehee and Sander in 1996. Their result on the stable manifold theorem is generalised and simplified; the proofs no longer use any functional analysis. Then comes an original “non-autonomous” version of the previous results, yielding–besides Pesin’s invariant laminations–seemingly unrelated results on invariant manifolds and conjugacies, presented in the end after a basic example.