 05111 S.V. Gonchenko, I.I. Ovsyannikov, C. Simo, D. Turaev
 Threedimensional Henonlike maps and wild Lorenzlike
attractors
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Mar 17, 05

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Abstract. We discuss a rather new phenomenon in chaotic dynamics connected
with the fact that some threedimensional diffeomorphisms can possess
wild Lorenztype strange attractors. These attractors persist
for open domains in the parameter space. In particular, we
report on the existence of such domains for a threedimensional
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 Lorenzlike 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.
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