The construction of one unstable manifold for the dissipative Henon mapping

The unstable manifold of a saddle point of the Henon mapping is constructed analytically via a contraction mapping, for a range of parameter values where the second fixed point is a stable node. One invariant piece of this manifold connects the saddle with the second fixed point. Rigorous error bounds are derived for the each step of the iterative procedure. It is demonstrated that an algebraic approximation with known accuracy can be given of the unstable manifold.