05-111 S.V. Gonchenko, I.I. Ovsyannikov, C. Simo, D. Turaev

Three-dimensional Henon-like maps and wild Lorenz-like attractors (4810K, LaTeX file with PS figures) Mar 17, 05

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Abstract. We discuss a rather new phenomenon in chaotic dynamics connected with the fact that some three-dimensional diffeomorphisms can possess wild Lorenz--type strange attractors. These attractors persist for open domains in the parameter space. In particular, we report on the existence of such domains for a three-dimensional Henon map (a simple quadratic map with a constant Jacobian which occurs in a natural way in unfoldings of several types of homoclinic bifurcations). Among other observations, we have evidence that there are different types of Lorenz-like attractors domains in the parameter space of the 3D Henon map. In all cases the maximal Lyapunov exponent is positive. Concerning the next Lyapunov exponent there are open domains where it is definitely positive, other where it is definitely negative and, finally, open domains where it cannot be distinguished numerically from zero (i.e., its absolute value is below some tolerance ranging between 0.00001 and 0.000001). Furthermore, several other kinds of interesting attractors have been found in this family of 3D Henon maps.

Files: 05-111.src( 05-111.keywords , lorh3d.tex , lorhfigs.zip.mm )