Abstract
Part I of this paper has been devoted to properties of the different Julia set configurations, generated by the complex map TZ: z = z2 − c, c being a real parameter, −1/4 < c < 2. These properties were revisited from a detailed knowledge of the fractal organization (called “boxwithin-
a-box ”), generated by the map x = x2 − c with x a real variable. Here, the second part deals with an embedding of TZ into the two-dimensional noninvertible map T : x = x2 + y − c;
y = γy + 4x2y, γ ≥ 0. For γ = 0, T is semiconjugate to TZ 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.
Lingua originale | English |
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pagine (da-a) | 3235-3282 |
Numero di pagine | 48 |
Rivista | International Journal of Bifurcation and Chaos in Applied Sciences and Engineering |
Volume | 19 |
DOI | |
Stato di pubblicazione | Pubblicato - 2009 |
Keywords
- Global bifurcations
- Julia set
- Noninvertible maps
- Stability