A model function for polynomial rates in discrete dynamical systems Original Research Article

In this paper, we construct a one-dimensional map with a nonhyperbolic 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 nonhyperbolic fixed point with one-dimensional center manifold.