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