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- W2000740947 abstract "Define the quadratic family of order two as Fµ(x,y) = (y,-x2 + µx), where µ is a real parameter. The boundary of the basin of attraction of the fixed point at ∞ is an invariant curve for µ 4. Perturbations of Fµ with µ≠4 were studied in Romero et al (2001 Discrete Continuous Dynam. Syst. 7 35) (also in higher dimension), where it was proved that these situations persist. Now we study perturbations of the bifurcation point µ = 4, where the explosion of the basin, B∞, occurs. We prove that either there exists a connected invariant curve J contained in the boundary of the basin, or the set of critical points is a subset of B∞ and the boundary has uncountably many components accumulated by the pre-images of the analytic continuation of the fixed point at the origin. The curve J undergoes a fractalization process until it ceases to exist." @default.
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- W2000740947 date "2001-10-22" @default.
- W2000740947 modified "2023-09-26" @default.
- W2000740947 title "Perturbations of the quadratic family of order two" @default.
- W2000740947 cites W2068251420 @default.
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- W2000740947 doi "https://doi.org/10.1088/0951-7715/14/6/312" @default.
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