Preprint of the project: DFG research group "Spectral analysis, asymptotic distributions and stochastic dynamics"

Numerical approximation and spectral analysis of infinite-dimensional dynamical systems

03-007 Thorsten Hüls.
A model function for polynomial rates in discrete dynamical systems


In this paper we construct a one-dimensional map with a non hyperbolic fixed point at zero for which the orbits converging to zero and the solution of the associated variational equation can be determined explicitly. We extend the construction to parameterized systems where the fixed point undergoes bifurcations. Applications are indicated to heteroclinic orbits that connect a hyperbolic to a non hyperbolic fixed point with one-dimensional center manifold.