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- W2111627123 abstract "Part I of this paper has been devoted to properties of the different Julia set configurations, generated by the complex map T Z : z′ = z 2 - c, c being a real parameter, -1/4 < c < 2. These properties were revisited from a detailed knowledge of the fractal organization (called box-within-a-box), generated by the map x′ = x 2 - c with x a real variable. Here, the second part deals with an embedding of T Z into the two-dimensional noninvertible map [Formula: see text]; y′ = γ y + 4x 2 y, γ ≥ 0. For [Formula: see text] is semiconjugate to T Z in the invariant half plane (y ≤ 0). With a given value of c, and with γ decreasing, the identification of the global bifurcations sequence when γ → 0, permits to explain a route toward the Julia sets, from a study of the basin boundary of the attractor located on y = 0." @default.
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- W2111627123 date "2009-10-01" @default.
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- W2111627123 title "FROM THE BOX-WITHIN-A-BOX BIFURCATION STRUCTURE TO THE JULIA SET PART II: BIFURCATION ROUTES TO DIFFERENT JULIA SETS FROM AN INDIRECT EMBEDDING OF A QUADRATIC COMPLEX MAP" @default.
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- W2111627123 doi "https://doi.org/10.1142/s021812740902475x" @default.
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