Nagashima H., Baba Y. — Introduction to chaos: physics and mathematics of chaotic phenomena :: Электронная библиотека попечительского совета мехмата МГУ

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Nagashima H., Baba Y. — Introduction to chaos: physics and mathematics of chaotic phenomena

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Название: Introduction to chaos: physics and mathematics of chaotic phenomena

Авторы: Nagashima H., Baba Y.

Аннотация:

This textbook is a basic introduction to chaos. It is written primarily for advanced undergraduate students in science but postgraduate students and researchers in mathematics, physics and other areas of science will also find the book useful .

Язык:

Рубрика: Физика/Нелинейная динамика, Хаос/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 169

Добавлена в каталог: 22.09.2005

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Предметный указатель

$f(\alpha)$ -method      108
$\varepsilon$ -neighbourhood      20
Accumulation point      120
Asymptotically      20
Attractor      77 85
Baker’s transformation      6
Belouzov — Zhabotinsky reation      9
Benard convection      114
Bernoulli shift      3
Binary transformation      3 16 35
Burst      65
Cantor set      92 109 119
Capacity dimension      91
Circle map      115
conjugate      37
Conservative system      71
Continuum      119
Continuum Hypothesis      1 19
Correlation dimension      94
Countable set      119
Crisis      60
Delta function      126
Dense      35
Dissipative system      71
Double pendulum      11 140
Elongation      6
Embedding dimension      86
entropy      27
Eventurally periodic      15
Feigenbaum constant      47
Feigenbaum route      42
Fixed point      13
Folding      6
Fractal      88 91
Frobenius — Perron relation      39
Generalized dimension      93
Global spectrum method      108
Gramm — Schmidt method      102
Hamilton system      83
Hamiltonian      76 84
Hausdorff dimension      84
Heaviside function      95 127
Henon map      87 96
Hopf bifurcation      42
Infimum      121
Information dimension      94
Initial condition, sensitivity to      5
Initial value      14
Inner measure      25 121
Intermittency chaos      42
Intermittent chaos      64
Invariant measure      38 133
Inverse image      26
Jensen’s Inequality      95
Kneading sequence      132
Koch curve      91
Laminar      64
Lap number      29
Lebesgue measurable      122
Lebesgue measure      122
Li — Yorke chaos      23
Li — Yorke theorem      13 22
Limit cycle      77
Liouville’s theorem      76

Logistic map      2 16 37 45 57 116 127 133
Lorenz model      78
Lorenz plot      99
Lower limit      120
Lyapunov dimension      101
Lyapunov exponent      11
Lyapunov number      35 40 82 101
Lyapunov spectrum      83
Magnon chaos      86
MAP      1 14
Maximum Lyapunov number      41
Measurable      122
Measure      122
Mobius function      17 117
Mobius inversion formula      17 117
Newton method      59 129
Normal number      36 123
Null set      24 122
Observable chaos      24
One-dimensional map      2 9 13 80
Open cover      26
Orbit      14 72
Outer measure      25 121
Period      13
Period doubling      45
Period k      14
Period k point      13
Periodic orbit      16
Phase orbit      72
Phase plane      72
Phase space      72
Pitchfork bifurcation      42
Pitchfork bifurcation, consecutive      42
Poincare return map      80
Poincare section      79
Pomeau — Manneville route      42
Potential chaos      41
Randomly irrational number      38
Rossler model      78
Saddle point method      111 139
Schwarz condition      50 54
Schwarz derivative      54
Scrambled set      23
Self-similar structure      91
Sharkovski’s theorem      13 15
Singularity      107
Spline Function      82
Stability      20
Stable      21 54
Stationary orbit      34 45
Strange Attractor      10 78 81 88
Superstable periodic orbit      31
Supremum      121
Tangent bifurcation      42 58
Tent map      3 15 26 37 42 123
Topological entropy      11 25 27 33 131
topology      27
Transformation      14
Uniform distribution      36
Unobservable chaos      25
Unstable      21 54
Unstable system      40
Upper limit      120
van der Pol equation      77
Window      35 57

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