TY - JOUR
T1 - From the box-within-a-box bifurcations organization to the Julia set. Part II: Bifurcation routes to different Julia sets from an indirect embedding of a quadratic complex map
AU - Agliari, Anna
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - Global bifurcations
KW - Julia set
KW - Noninvertible maps
KW - Stability
KW - Global bifurcations
KW - Julia set
KW - Noninvertible maps
KW - Stability
UR - http://hdl.handle.net/10807/28127
U2 - 10.1142/S021812740902475X
DO - 10.1142/S021812740902475X
M3 - Article
SN - 0218-1274
VL - 19
SP - 3235
EP - 3282
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
ER -