Index

accessible point, 29

acyclic, 30

allowable partition, 28

B, 35

B∞,

35

boundary scrambling

for dendrites, 50

for planar continua, 51

branched covering map, 68

branchpoint of f, 75

bumping

arc, 25

simple closed curve, 25

C(a, b), 38

Carath´ eodory Loop, 27

chain of crosscuts, 28

equivalent, 28

channel, 29

dense, 29, 57

completing a bumping arc, 25

C, 1

C∞,

1

conformal

external ray, 53

continuum

decomposable, 49

indecomposable, 49

convE (K), 35

convH(B ∩ K), 35

convex hull

Euclidean, 35

hyperbolic, 35

counterclockwise order

on an arc in a simple closed curve, 13

critical point, 74

crosscut, 25

shadow, 26

cutpoint, 51

CX , 53, 85

D, 38

defines variation near X, 50

degree, 13

degf (a), 75

degree(g), 13

degree(fp), 16

∂ boundary operator, 2

D∞,

27

dendrite, 6

domain

attracting, 52

Fatou, 52

parabolic, 52

Siegel, 52

embedding

orientation preserving, 19

essential crossing, 29

Et, 29

exit continuum, 51

for a general puzzle-piece, 53

external ray, 29

end of, 29

essential crossing, 29

landing point, 29

non smooth, 53

smooth, 53

fixed point

for positively oriented maps, 63

non-rotational, 53

(f, X, η), 50

G, 38

g, 38

g, 35

Γ, 38

gap, 37, 68

general puzzle-piece, 53

geodesic

hyperbolic, 38

geometric outchannel

negative, 50

positive, 50

hull

hyperbolic, 37

95