ANALYSIS OF THE STABILITY DOMAIN FOR THE HENON MAP

To give an analytic estimate of the stability domain of nonlinear syst ems has been a subject of intense theoretical studies. Up to now, even for the simple case of the one-dimensional Henon map, one has not bee n able to determine the border of the stability domain using analytic tools. On the other hand this estimate can easily be found by tracking through the map. A promising new attempt is presented here to estimat e the dynamic aperture for the Henon map via following the invariant m anifolds of its hyperbolic fixed point.