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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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Periodic orbit 2 Perron theorem 58 Perron — Frobenius theorem 57 Piecewise-monotone map 170 Plaque 139 Poincare 71 Poincare classification theorem 158 Poincare map 22 72 Poincare recurrence theorem 72 103 Point 2 162 198 Point, attracting 10 192 Point, irrationally neutral 192 Point, rationally neutral 192 Point, repelling 10 192 Point, superattracting 192 Pointwise almost periodic homeomorphism 47 Polynomial recurrence theorem 102 Pontryagin duality theorem 95 Positive semiorbit 2 Positive upper density 101 Positively expansive 35 Positively recurrent point 29 Postcritical set 204 Presentation 67 Primitive matrix 57 79 104 Primitive substitution 64 90 Primitive transformation 73 Probability measure 70 Probability space 70 Product formula 60 Product, direct 3 Product, skew 3 Product, structure, local 129 Projection 3 139 140 Proximal points 45 Pseudo-orbit 110 Quadratic map 9 35 171 176 178 179 182 205 Quotient 91 Radon — Nikodym derivative 86 Radon — Nikodym theorem 86 Ramsey 48 Ramsey theory 48 Random behavior 23 Random variable 79 Rational map 191 Rational map, degree of 193 Rationally neutral periodic point 192 rectangle 134 Recurrence, measure-theoretic 71 Recurrence, topological 29 72 Recurrent point 29 72 Reducible matrix 57 refinement 208 Refining sequence of partitions 215 Regular measure 71 Relatively dense subset 30 Repelling periodic point 192 Repelling point 9 Return time 22 Riemann sphere 191 Riemannian manifold 106 140 Riemannian metric 106 139 Riemannian volume 140 Riesz 80 85 Riesz representation theorem 85 Right translation 4 Robbin 134 Robinson 134 Rokhlin 97 Rokhlin metric 212 Rokhlin — Halmos lemma 96 Rotation number 154 Rotation, entropy of 218 Roush 63 Saddle-node bifurcation 184 Sarkozy 103 Schwarzian derivative 178 Search engine 103 Self-similarity 202 Semiconjugacy 2 Semiconjugacy, topological 28 Semiflow 2 Semiorbit, negative 2 Semiorbit, positive 2 Sensitive dependence on initial conditions 23 117 sep 37 Separated set 37 Sequence of partitions, generating 215 Sequence of partitions, refining 215 Sf(x) 178 SFT 56 Shadowing 107 111 113 Shannon 220 Shannon — McMillan — Breiman theorem 217 Shannon — Parry measure 220 Sharkovsky ordering 162 Sharkovsky theorem 163 Shift 5 7 54 60 Shift edge 57 Shift equivalence, strong 62 Shift, entropy of 219 Shift, equivalence 62 Shift, one-sided 7 Shift, two-sided 7 Shift, vertex 8 56 Shishikura theorem 200 Signed lexicographic ordering 172 Simply transitive 180 192 Sinai 208 216 Singer theorem 179 Skew product 3 140 Smale 133 Smale's spectral decomposition theorem 133 Smooth measure 151 Sofic subshift 66 Solenoid 18 35 36 44 45 108 128 Space average 84 Space, metric 28 span 37 Spanning set 37 Spectral measure 98 Spectrum, cone 115 Spectrum, continuous see continuous spectrum Spectrum, discrete see discrete spectrum stable Spectrum, distribution 108 Spectrum, foliation 14 130 Spectrum, manifold 14 118 122 Spectrum, manifold, local 121 Spectrum, set 151 Spectrum, subspace 108 Stationary sequence 79 Stochastic matrix 58 78 104 Stochastic process 79 Strange Attractor 25 Strong mixing transformation 74 Strong transversality condition 134 Structural stability 108 117 131 Structural stability theorem 134 Struturally stable diffeomorphism 117 Submanifold 106 139 Submanifold, embedded 139 Subshift 8 55 134 Subshift of finite type 56 Subshift, entropy of 219 Subshift, generating function of 60 Subshift, one-sided 55 Subshift, soric 66 Subshift, topological entropy of 60 Subshift, two-sided 55 Subshift, zeta function of 61 Substitution 64 Substitution, constant length 64 Substitution, irreducible 64 Substitution, primitive 64 90 Sullivan 205 Superattracting periodic point 192 Supp 72 90 Support 72 Suspension 21 Symbol 7 54 Symbolic dynamics 6 54 Symmetric difference 73 Syndetic subset 30 Szemeredi 103 Szemeredi theorem 103 Tangent bundle 138 Tangent map 138 Tangent space 138 Tangent vector 138 Tent map 114 176 Terminal vertex 9 Theorem, Anosov's shadowing 113 Theorem, Birkhoffergodic 82 Theorem, Bowen — Lanford 61 Theorem, Curtis — Lyndon — Hedlund 55 Theorem, Denjoy 160 Theorem, Douady — Hubbard 206 Theorem, Fatou 204 Theorem, Frobenius 59 Theorem, Furstenberg — Weiss 49 Theorem, Hadamard — Perron 118 Theorem, Halmos — von Neumann 96 Theorem, Kolmogorov — Sinai 216 Theorem, Koopman — von Neumann 99 Theorem, Krein — Milman 86 Theorem, Krylov — Bogolubov 85 Theorem, maximal ergodic 82 Theorem, Montel 197 Theorem, multiple recurrence 103 Theorem, Perron 58 Theorem, Perron — Frobenius 57 Theorem, Poincare classification 158 Theorem, Poincare recurrence 72 Theorem, polynomial recurrence 102 Theorem, Pontryagin duality 95 Theorem, Riesz representation 85 Theorem, Sarkoezy 103 Theorem, Shannon — McMillan — Breiman 217 Theorem, Sharkovsky 163 Theorem, Shishikura 200 Theorem, Singer 179 Theorem, Smale's spectral decomposition 133 Theorem, structural stability 134 Theorem, Szemeredi 103 Theorem, van der Waerden 49 Theorem, von Neumann ergodic 80 Theorem, Weyl 89 Theorem, Williams 62 Time average 84 88 Time-t map 2 Times-m map 5 Topological conjugacy 28 39 Topological dynamical system 28 Topological dynamics 28 Topological entropy 36 37 60 116 125 Topological group 4 95 Topological Markov chain 56 Topological mixing 33 76 Topological properties 28 Topological recurrence 29 72 Topological semiconjugacy 28 Topology, 138 Toral automorphism see hyperbolic toral Toral automorphism, aperiodic 96 Toral automorphism, automorphism transformation 70 Toral automorphism, derivative 72 Toral automorphism, entropy of 215 Toral automorphism, ergodic 73 Toral automorphism, Gauss see Gauss transformation Toral automorphism, induced 73 Toral automorphism, linear fractional 180 Toral automorphism, measure-preserving 70 Toral automorphism, mixing 74 Toral automorphism, Moebius 180 192 Toral automorphism, non-singular 70 Toral automorphism, primitive 73 Toral automorphism, strong mixing 74 Toral automorphism, uniquely ergodic 87 Toral automorphism, weak mixing 75 Transition probability 78 Transitivity 31 33 76 88 Translation 90 Translation, group 4 Translation, left 4 Translation, right 4 Translation-invariant metric 44 Transversal 139 Transversal, local 139 Transverse 139 Transverse homoclinic point 125 Transverse submanifolds 122 Transversely absolutely continuous foliation 145 Trapping region 25 Turning point 170 Uniform convergence 88 Uniformly distributed 89 90 Unimodal map 170 Uniquely ergodic 87—90 Unitary operator 80 Unstable cone 115 Unstable distribution 108 Unstable foliation 14 130 Unstable manifold 14 118 122 Unstable manifold, local 121 Unstable set 151 Unstable subspace 108 Upper density 99 Van der Waerden's theorem 49 Var(f) 160 Variational principle for metric entropy 221 Vector field 107 139 Vector, non-negative 57 Vector, positive 57 Vertex shift 8 56 Vertex shift, one-sided 8 Vertex shift, two-sided 8 Vertex, terminal 9 von Neumann 80 von Neumann ergodic theorem 80 Wandering domain 205 Wandering interval 173 Weak mixing 75 97 100 152 Weak mixing, flow 75 Weak mixing, transformation 75 Weak topology 97 Weak* topology 85 Weiss 49 135 Weiss, even system of 66 Weyl theorem 89 Whitney embedding theorem 111 Wiener lemma 98 Williams 63 Wolff 205 Word 7 Word, allowed 8 56 Word, forbidden 8 56 Yorke 164 Zeta function 60 Zeta function, rational 61 [x, y] 128
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