Abstract
The complex Henon map H(z,ω) = (z 2 + c + dω, dz) is the complex version of the real map studied by Henon [H]. It is also the first interesting generalization of the quadratic polynomial P c (z) = z 2 + c to two complex variables. There are some essential differences between the one and two complex variables mappings. In particular, the bifurcation locus of the Henon map is not the connectivity locus of the Julia set as in the one-complex-variable case. We will relate the complex mapping to the mapping of two real variables and to one-complex-variable mappings. We will outline a computer assisted proof to compute the location of one particular type of bifurcation and describe its relationship with attracting orbits. The study of the bifurcation locus of the complex Henon map is particularly important because it gives insight into the chaotic behavior of the real Henon map.
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Gavosto, E.A. (2000). Bifurcations of the Complex Henon Map. In: de la Llave, R., Petzold, L.R., Lorenz, J. (eds) Dynamics of Algorithms. The IMA Volumes in Mathematics and its Applications, vol 118. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1274-4_7
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DOI: https://doi.org/10.1007/978-1-4612-1274-4_7
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