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Afraimovich V.S., Hsu S.-B. — Lectures on Chaotic Dynamical Systems
Afraimovich V.S., Hsu S.-B. — Lectures on Chaotic Dynamical Systems



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Название: Lectures on Chaotic Dynamical Systems

Авторы: Afraimovich V.S., Hsu S.-B.

Аннотация:

"This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics." The book will help readers who are not familiar with nonlinear dynamics to understand and enjoy sophisticated modern monographs on dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.


Язык: en

Рубрика: Физика/Динамические системы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 353

Добавлена в каталог: 22.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\sigma$-algebra      98
Abels formula      219
Absolutely continuous invariant set      130
Absorbing region      9
Andronov — Hopf bifurcation      158 159
Andronov — Hopf — Neimark — Sacker bifurcation      18 159
Annulus principle      16 18 225
Anosov diffeomorphism      113
Arnold tongue      20 84
Attractor      6 9 10 11
Ball of dissipation      7
Belitskij theorem      207
Belykh map      220 h
Benedicks — Carleson result      149
Bernoulli shift (scheme)      38 42
Bernoulli shift (scheme), one-sided      45
Bernoulli shift (scheme), two-sided      45
Bifurcation surface      94 95 97
Bipermutative cellular automation      54
Birkhoff ergodic theorem      99
Borel $\sigma$-algebra      98
Borel set      98
Box dimension      59 63
Box dimension, lower      65
Box dimension, upper      65
Brouwer theorem      229 254
Bykov contour      205 206
Cantor set      21
Cellular      3 42
Cellular automata      3 42
Chaotic repellers      195
Chebyshev polynomial      215
Chirikov map      151
Chua attractor      151
Closed invariant curve      15
Codimension-one bifurcation      157
Codimension-two bifurcation      235
Collet — Eckmann condition      106 108
complexity      27 242
Cone family      245 246 248
Correlation dimension      36 213 220 224
Correlation integral      224
Coupled map lattice      214 215 220 221
Critical saddle-node      178 180 183
Cylinder      39 48
Delay coordinate algorithm      33
Destruction of two dimensional tori      182
Discritical inverse node      217
Discritical node      216
Dissipative      7 173 235
Dissipative separatrix map      17 161 173 235
Doubling transformation      96
Duffing equation      8 171
Dyadic adding machine      91
Dynamical chaos      5
Equilibrium      10
Ergodic      97
Established motion      9
Expansive      6
Expansive map      48
Feigenbaum attractor      92 95
Feigenbaum universality      95
Filiation      267
Fixed point      4 11
Fractal dimension      27
Fundamental region      181
Generalized hyperbolic attractor      153
Geometric construction      23 66
Geometric finale horseshoes      112 210
Hadamard conditions      109 150
Hausdorff dimension      64 66
Henon map      109
Homoclinic      140
Homoclinic orbit      84 155 192
Homoclinic tangency      148 149 183
Hyperbolic attractor      90
Hyperbolic automorphism      113
Hyperbolic repeller      90
Hyperbolic set      149 211
Immediate basin      90
Indicator function      100
Infinitely renormalizable      89 91
Invariant      4
Invariant measure      97
Invariant tori      15
Jacobson theorem      108
Kneading invariants      76 77 87
Kneading series      79
Kneading theory      76
Kolmogorov complexity      242
Lambda lemma      122 130
Leading direction      228
Lebesgue density point      108
Lebsgue measure      98
Limit cycle      13
Liouville's formula      57
Local bifurcation of equilibrium      194
Logistic map      3
Lorentz attractor      252
Lorentz system      8
Lorentz-type map      85
Lozi map      151
Lyapunov dimension      36
Lyapunov exponents      106 213
Mane Theorem      30
Markov partition      75 202
Markov processes      105
Maximal attractor      9
Measurable set      98
Melnikov function      163
Minimum principle      89
Mobius band      189
Moran construction      66
Morse — Smale system      155
Multiplicative ergodic theorem of Oseledec      216
Multiplier      11 13
Neutral      90
Newhouse phenomena      148
Newhouse region      149
Nonlocal bifurcation      160
Nonwandering      4 84
Observable      1
Orbit      4
Oriented graph      53
Period-doubling bifurcation      93
Period-doubling cascade      147 173
Periodic orbit      4 156 165 189
Periodic perturbation      14 155 157
Periodic point      12
Perron — Frobenius equation      124 125
Perron — Frobenius operator      125
Perron — Frobenius theorem      66 127
Phase space      3
Poincare map      15
Poincare recurrence theorem      121
Poincare — BirkhofF problem      121
Pointwise dimension      223
Pointwise dissipative      174
Poisson bracket      171
Positive semi-trajectory      4
Probability measure      98
Quadratic homoclinic tangency      183
Quadratic tangency      140
Quasi-hyperbolic      152
Reaction-diffusion equation      116
Renormalization      88
Rotation number      20 84
s-critical      221
S-unimodal map      2
Saddle node      180
Saddle-focus point      205
Saddle-node bifurcation      146 158 178
Schwarzian derivative      89
Sensitive dependence on initial condition      6
Separatrix map      17
Sharkovski ordering      103
Sharkovsky theorem      83
Shilnikov's technique      123
Sine-Gordon      150
Smale attractor      24
Spectral decomposition theorem      153
Stable set      47
Stable subspace      115
Standard map      151
Steady-stable solution      143
Steady-state equation of sine-Gordon      150
Strange Attractor      19
Strongly transitive      70
Structurally stable      112
Subshifts of finite type      52
Taken's ratio      35
Tent map      40
Time-correlation      105
Topological entropy      6 27 79
Topological Markov chain      52 243
Topological mixing      6 56
Topological pressure      59
Topological transitive      7
Topological transitivity      68
Trajectory      4
Transient process      9
Transition matrix      53 243
Unimodal map      86
Unstable set      47
Unstable subspace      115
Wild hyperbolic set      149
Zaslavsky map      16 19 112 152 239
Zeta function      57
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