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Brin M., Stuck G. — Introdution to dynamical system
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Название: Introdution to dynamical systemАвторы: Brin M., Stuck G. Аннотация: This book provides a broad introduction to the subject of dynamical systems, suitable for a one or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to areas such as number theory, data storage, and internet search engines.
Язык: Рубрика: Физика /Динамические системы /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2002Количество страниц: 240Добавлена в каталог: 18.05.2005Операции: Положить на полку |
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Предметный указатель
Flip bifurcation 185 Flow 2 19 Flow, continuous 28 Flow, differentiable 107 Flow, entropy of 41 Flow, gradient 20 Flow, measurable 70 74 Flow, measure preserving 70 Flow, under a function 21 Flow, weak mixing 75 Fold bifurcation 185 Foliation 139 Foliation, absolutely continuous 144 Foliation, coordinate chart 139 Foliation, leaf of 139 Foliation, stable 14 130 Foliation, transversely absolutely continuous 145 Foliation, unstable 14 130 Forbidden word 8 Forward invariant set 2 Fourier series 78 Fractal 191 193 202 Frobenius theorem 59 Full m-shift 55 Full measure 69 Full one-sided shift 7 33 Full shift 35 36 Full two-sided shift 7 33 Function, analytic 191 Function, ceiling 21 Function, essentially invariant 73 Function, generating 60 Function, Hamiltonian 21 Function, Lyapunov 20 Function, meromorphic 191 Function, strictly invariant 74 Function, zeta 60 Furstenberg 49 101—103 G-extension 88 Gauss 11 Gauss measure 12—13 90—94 Gauss transformation 11—13 90—94 Generalized eigenspaces 42 Generating function 60 Generating sequence of partitions 215 Generator, one-sided 216 Generator, two-sided 216 Generic bifurcation 183 Generic point 88 Global stable manifold 122 Global unstable manifold 122 Google, 103 Gradient flow 20 Graph transform 119 Group of characters 95 Group, automorphism 5 Group, dual 95 Group, endomorphism 5 14 Group, extension 88 Group, topological 4 95 Group, translation 4 35 45 87 h(f) 37 Haar measure 88 hadamard 54 Hadamard — Perron theorem 118 Halmos 97 Halmos — von Neumann theorem 96 Hamiltonian function 21 Hamiltonian system 20 Hedlund 55 Henon attractor 25 Heteroclinic point 128 Heteroclinically related 133 Higher block presentation 56 67 Hoelder constant 143 Hoelder continuity 142 143 HoElder exponent 143 Holonomy map 145 Homeomorphism 28 Homeomorphism of the circle 153 Homeomorphism, distal 45 Homeomorphism, equicontinuous 45 Homeomorphism, expansive 35 40 Homeomorphism, minimal 29 Homeomorphism, pointwise almost periodic 47 Homoclinic point 125 Hopf 151 Hopf's argument 141 Horseshoe 34—36 108 124 125 128 Horseshoe, entropy of 125 Horseshoe, linear 15 16 Horseshoe, non-linear 124 Hubbard 205 Hyperbolic attractor 18 Hyperbolic dynamical system 15 106 Hyperbolic fixed point 110 Hyperbolic periodic point 110 Hyperbolic set 108 Hyperbolic toral automorphism 14 22 33 35 36 41 108 130 135 Hyperbolic toral automorphism is mixing 77 Hyperbolic toral automorphism, metric entropy of 221 Hyperbolicity 106 108 I(C) 210 i(x) 170 Immediate basin of attraction 192 Inclination lemma 123 Independent partitions 209 Induced transformation 73 information 210 Integrable distribution 139 Integrable foliations 151 Integral hull 151 Internet 103 Intersection of partitions 208 Intersymbol interference 67 Invariant kneading 173 Invariant measure 70 85 Invariant set 2 IP-system 49 Irrational circle rotation 4 33 77 87 90 Irrationally neutral periodic point 192 Irreducible matrix 57 Irreducible substitution 64 Isolated fixed point 10 Isometric extension 41 46 Isometry 28 34 36 114 Isometry, entropy of 38 Isomorphism 3 Isomorphism of subshifts 55 Isomorphism of topological dynamical systems 28 Isomorphism, measure-theoretic 70 Itinerary 54 170 J(R) 193 Jacobian 145 Julia set 193 200 k-step SFT 56 Katok 111 Kim 63 Kneading invariant 173 Kolmogorov 208 216 Kolmogorov — Sinai theorem 216 Koopman — von Neumann theorem 99 Krein — Milman theorem 86 Krylov — Bogolubov theorem 85 l-modal map 170 Lag 63 Lambda lemma 123 Lanford 61 LAP 170 Leader 81 Leaf 139 Leaf, local 139 Lebesgue number 224 Lebesgue space 71 Left translation 4 Lemma inclination 123 Lemma, lambda 123 Lemma, Rokhlin — Halmos 96 Length distortion 180 Li 164 Linear fractional transformation 180 Linear functional 85 Lipshitz function 160 Local coordinate system 106 Local leaf 139 Local product structure 129 Local stable manifold 121 Local transversal 139 Local unstable manifold 121 Locally maximal hyperbolic set 128 Locally maximal invariant set 16 LOG 209 Lorenz 26 Lorenz attractor 25 Lyapunov exponent 23 Lyapunov function 20 Lyapunov metric 109 Lyndon 55 Main cardioid 206 Mandelbrot set 206 Mane 134 Manifold, differentiable 106 137 Manifold, Riemannian 106 140 Manifold, stable 14 118 122 Manifold, unstable 14 118 122 Map, covering 153 Map, expanding 5 Map, first return 72 Map, l-modal 170 Map, measurable 70 Map, measure preserving 70 Map, non-singular 70 Map, piecewise-monotone 170 Map, Poincare 22 72 Map, quadratic 9 35 171 176 178 179 182 205 Map, rational 191 Map, tent 176 Map, unimodal 170 Markov chain 78 104 105 Markov graph 164 165 Markov measure 57 78 104 105 219 Markov partition 134 Matrix, adjacency 56 Matrix, composition 65 Matrix, irreducible 57 Matrix, non-negative 57 Matrix, positive 57 Matrix, primitive 57 79 Matrix, reducible 57 Matrix, shift-equivalent 62 Matrix, stochastic see stochastic matrix Matrix, strong shift-equivalent 62 Maximal almost periodic set 47 Maximal ergodic theorem 82 McMillan 217 Measurable flow 70 74 Measurable map 70 Measurable set 70 Measure 69 Measure of maximal entropy 224 Measure, absolutely continuous 86 Measure, Bernoulli 79 219 Measure, Borel 72 Measure, conditional 92 Measure, Dirac 86 Measure, ergodic 86 Measure, Gauss see also Gauss measure Measure, Haar 88 Measure, invariant 70 85 Measure, Markov 57 78 see Measure, regular 71 Measure, Shannon — Parry 220 Measure, smooth 151 Measure, space 69 Measure, spectral 98 Measure-preserving flow 70 Measure-preserving transformation 70 Measure-theoretic entropy 213 215 Measure-theoretic extension 70 Measure-theoretic isomorphism 70 Meromorphic function 191 Metric, adapted 109 Metric, entropy 213 215 Metric, Lyapunov 109 Metric, Riemannian 106 139 Metric, space 28 Minimal, action of a group 49 Minimal, dynamical system 4 29 Minimal, homeomorphism 29 Minimal, period 2 Minimal, set 29 90 Minimum principle 179 Mixing 74 77 Mixing transformation 74 Mixing, weak 75 100 152 mod 0 71 Modified frequency modulation 68 Modular function 198 Moebius transformation 180 192 Monochromatic 51 Montel theorem 197 Morse sequence 64 Multiple recurrence theorem 103 Multiple recurrence, topological 49 Multiplier 192 n-leader 81 Negative semiorbit 2 Newton method 196 Nilmanifold 130 Non-atomic Lebesgue space 71 Non-linear horseshoe 124 Non-negative definite sequence 97 Non-singular map 70 Non-singular transformation 70 Non-wandering point 29 Normal family 193 197 Normal family at a point 193 Normal number 84 Null set 69 Number theory 49 92 103 NW(f) 29 114 Omit a point 197 One-parameter group 107 One-sided shift 35 Orbit 2 Orbit, dense 23 32 Orbit, periodic 2 Orbit, uniformly distributed 23 89 P-graph 165 PARRY 220 Partition 208 Partition of an interval 164 Partition, boundary of 222 Partition, Markov 134 Partitions, independent 209 Pendulum 19 per(f) 114 Period 2 Period, minimal 2 Period-doubling bifurcation 185
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