Mixing and relaxation dynamics of the Henon map at the edge of chaos

The mixing properties (or sensitivity to initial conditions) and relaxation dynamics of the Henon map, together with the connection between these concepts, have been explored numerically at the edge of chaos. It is found that the results are consistent with those coming from one-dimensional dissipative maps. This constitutes the first verification of the scenario in two-dimensional cases and obviously reinforces the idea of weak mixing and weak chaos. Keywords: Nonextensive thermostatistics, Henon map, dynamical systems