Subject Index
551
Lorenz gas, 142
Lyapounov exponent, 13, 36, 38, 40, 150
fast indicator, 140
M
Magnetic dipole, 111
Magnetic vector potential, 111
Manifolds
invariant, 116
stable, 55, 103, 119, 126, 265
unstable, 55, 103, 119, 126, 265
Maps
area-preserving, 47
baker’s, 96, 196
scars, 196
cometary, 95
de Vogelaere, 74
Fermi, 94
Kepler, 95
non-twist, 96
quadartic, 94
quadratic, 49, 72
renormalization, 49, 84
fixed points, 90
scattering, 116
spectral properties, 96
standard, 48, 57, 65, 80, 94
symplectic, 103
tangent, 54, 71, 72, 75
twist, 47–94
integrable, 66
nonintegrable, 69
universal, 48, 70, 83, 94
whisker, 94
Markov tree, 84
Mathieu equation, 356
Matrix
complex Hermitian, 435, 438, 441, 474
invariant measure, 435, 437, 440
invariant metric, 435, 437
polar form, 436, 437
complex Hermitian (2×2)
invariant measure, 438
Floquet, 343
general unitary, 444
invariant measure, 444
invariant metric, 444
volume of measure, 444
Hermitian, 433, 440
invariant measure, 440
identities, 448
orthogonal, 158, 273, 433, 446, 447
invariant measure, 447
invariant metric, 447
parametric representation, 446
volume of measure, 447
quaternion, 455, 501
quaternion real, 438, 440, 441
invariant measure, 439, 440
invariant metric, 439, 440
polar form, 439, 440
real symmetric, 433, 435, 441
invariant measure, 433, 434, 440
invariant metric, 433, 434
N×N , 158
polar form, 434, 435
symmetric unitary, 442, 443
invariant measure, 442
invariant metric, 442
volume of measure, 443
symplectic unitary, 445
invariant measure, 445
invariant metric, 445
unitary, 441, 446
complex symmetric, 441
definition, 441
eigenphases, 442
extremize information, 276
from Hermitian matrix, 493
invariant measure, 275, 446
invariant metric, 275, 442
parametric form, 441
parametric representation, 274
relation of Hermitian matrix, 279
symplectic, 441
volume of invariant measure, 447,
452, 453
Maxwell-Boltzmann distribution, 188, 192
Maxwell’s equations
definition, 515, 525
Gaussian units, 525
microwave billiards, 515
M-cycles, 59, 71
Measure
invariant, 158, 159, 474
GSE, 485
polar form, 160, 475
real symmetric matrix, 161
Metric
invariant, 159
GUE, 475
polar form, 160, 476
Metric, (ds) 2 , 157
Microwave driven hydrogen, 369
dynamic Anderson localization, 340
Microwave induced ionization
hydrogen , 369
551
Lorenz gas, 142
Lyapounov exponent, 13, 36, 38, 40, 150
fast indicator, 140
M
Magnetic dipole, 111
Magnetic vector potential, 111
Manifolds
invariant, 116
stable, 55, 103, 119, 126, 265
unstable, 55, 103, 119, 126, 265
Maps
area-preserving, 47
baker’s, 96, 196
scars, 196
cometary, 95
de Vogelaere, 74
Fermi, 94
Kepler, 95
non-twist, 96
quadartic, 94
quadratic, 49, 72
renormalization, 49, 84
fixed points, 90
scattering, 116
spectral properties, 96
standard, 48, 57, 65, 80, 94
symplectic, 103
tangent, 54, 71, 72, 75
twist, 47–94
integrable, 66
nonintegrable, 69
universal, 48, 70, 83, 94
whisker, 94
Markov tree, 84
Mathieu equation, 356
Matrix
complex Hermitian, 435, 438, 441, 474
invariant measure, 435, 437, 440
invariant metric, 435, 437
polar form, 436, 437
complex Hermitian (2×2)
invariant measure, 438
Floquet, 343
general unitary, 444
invariant measure, 444
invariant metric, 444
volume of measure, 444
Hermitian, 433, 440
invariant measure, 440
identities, 448
orthogonal, 158, 273, 433, 446, 447
invariant measure, 447
invariant metric, 447
parametric representation, 446
volume of measure, 447
quaternion, 455, 501
quaternion real, 438, 440, 441
invariant measure, 439, 440
invariant metric, 439, 440
polar form, 439, 440
real symmetric, 433, 435, 441
invariant measure, 433, 434, 440
invariant metric, 433, 434
N×N , 158
polar form, 434, 435
symmetric unitary, 442, 443
invariant measure, 442
invariant metric, 442
volume of measure, 443
symplectic unitary, 445
invariant measure, 445
invariant metric, 445
unitary, 441, 446
complex symmetric, 441
definition, 441
eigenphases, 442
extremize information, 276
from Hermitian matrix, 493
invariant measure, 275, 446
invariant metric, 275, 442
parametric form, 441
parametric representation, 274
relation of Hermitian matrix, 279
symplectic, 441
volume of invariant measure, 447,
452, 453
Maxwell-Boltzmann distribution, 188, 192
Maxwell’s equations
definition, 515, 525
Gaussian units, 525
microwave billiards, 515
M-cycles, 59, 71
Measure
invariant, 158, 159, 474
GSE, 485
polar form, 160, 475
real symmetric matrix, 161
Metric
invariant, 159
GUE, 475
polar form, 160, 476
Metric, (ds) 2 , 157
Microwave driven hydrogen, 369
dynamic Anderson localization, 340
Microwave induced ionization
hydrogen , 369