Index a point, 78 accessible boundary point, 48 accumulation set, 69 affine transformations, 128 Arzela-Ascoli Theorem, 60 attracting, 63, 64, 66, 72 attracting cycle, 79 attracting fixed point, 4, 66 attracting periodic point, 63 attracting set, 38 attractive basin, 66, 79 attractive cycle, 66, 69 attractor, 38, 131 base of attraction, 38 basin boundary metamorphoses, 52 basin of attraction, 41 bifurcation, 7 bifurcation diagram, 11 bifurcation set, 81 Birkhoff, G. D., 51 Blanchard, P., 65, 77 Borel measure, 138 bounded density, 112 box dimension, 110 Branner, 58 Brolin, H., 77 Brooks, R., 77 Camacho, 65 canonical coordinates, 89 Cantor set, 14, 31, 71, 114 Caratheodory, 49 Cartwright and Littlewood, 51 Cayley, A., 77 cellular, 92 center of hyperbolic component, 86 chaos, 17 chaotic behavior, 57, 58 chaotic trajectory, 41 Collage Theorem, 135, 139 comparable net measures, 110 completely invariant, 60, 61, 62, 63,69 completely invariant components, 69 complex exponential, 22 computer graphics, 141 condensation set, 133, 134 condensation transformation, 134 connected, 73 connectivity, 69, 72 continued fractal, 117 continued fraction, 117 contraction, 112 contraction mappings, 130 contraction ratio, 112 contractivity factor, 135, 136 Cremer, 68 critical, 63 critical point, 58, 64, 66, 67, 69, 70, 71, 72, 77 critical value, 58, 78 cross section, 27 cycle, 6, 78 145

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