Dynamics of a Henon-Lozi-type map

We present and analyze a smooth version of the piecewise linear Lozi map. T he principal motivation for this work is to develop a map, which is better amenable for an analytical treatment as compared to the Henon map and is on e that still possesses the characteristics of a Henon-type dynamics. This p aper is a first step. It does the comparison of the Lozi map (which is a pi ecewise linear version of the Henon map) with the map that we introduce. Th is comparison is done for fixed parameters and also through global bifurcat ion by changing a parameter. If epsilon measures the degree of smoothness, we prove that, as epsilon --> 0, the stability and the existence of the fix ed points are the same for both maps. We also numerically compare the chaot ic dynamics, both in the form of an attractor and of a chaotic saddle. (C) 2001 Elsevier Science Ltd. All rights reserved.