Index

affine structure, 58

area construction, 152

Arnold-Liouville theorem, 70

Aubry-Mather theory, 106

average absolute curvature, 41

Baker's map, 135

Benford's Law, 25

billiard ball map, 33

Birkhoff conjecture, 95

Boltzmann's Hypothesis, 145

brachistochrone, 16

Buffon's needle problem, 38

Bunimovich billiards, 139

cat map, 137

caustic, 56

characteristic foliation, 48

complexity function, 29

configuration space, 3, 10

confocal conies, 53

Conley-Zehnder theorem, 106

Crofton formula, 37

cutting sequence, 27

cyclic configuration space, 100

Desargues theorem, 88, 162

diameter of a curve, 99

dihedral group, 116

Diophantine condition, 98

DNA geometric inequality, 41

elliptic coordinates, 53

equidistribution, 22

ergodic map, 138

evolute, 75

Fagnano trajectory,

Fermat principle, 12

Fibonacci numbers,

finite blocking, 121

Finsler metric, 14

four vertex theorem

Gauss-Bonnet theor

geodesic, 43, 67

Graves theorem, 74

Hamiltonian functio

Hamiltonian vector

Hilbert metric, 44

Hilbert's fourth pro

Huygens principle,

illumination problem

impact oscillator, 14

integrable map, 53,

invariant circle, 86

involute, 75

isochronal pendulum

isoperimetric inequa

KAM theory, 97

Klein-Beltrami mod

Kneser's lemma, 77

Lagrangian function

Lagrangian submani

Larmor radius, 18

length-area duality,

Lie algebra, 70

linkage, 10

Liouville form, 47