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Barreira L. — Dimension and Recurrence in Hyperbolic Dynamics
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Название: Dimension and Recurrence in Hyperbolic DynamicsАвтор: Barreira L. Аннотация: The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. More than half of the material appears here for the first time in book form, describing many recent developments in the area such as topics on irregular sets, variational principles, applications to number theory, measures of maximal dimension, multifractal nonrigidity, and quantitative recurrence. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1 editionГод издания: 2008Количество страниц: 300Добавлена в каталог: 14.04.2010Операции: Положить на полку |
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105 108 148 169 108 Automorphism 193 Automorphism, permutation 195 Backward Lyapunov exponent 240 Boundary, Markov partition 52 Boundary, stable 52 Boundary, unstable 53 Bowen's equation 25 Box dimension 8 Box dimension, lower 8 Box dimension, upper 8 Characteristic polynomial 206 Coding map 42 52 Cohomologous function 56 Conditional variational principle 147 155 167 Conformal map 41 43 59 Cover 104 Cover, Moran 20 29 38 44 85 87 225 Cylinder set 24 Decomposition, ergodic 226 Decomposition, multifractal 81 101 Degenerate spectrum 179 Diameter 7 Dimension, box 8 Dimension, Hausdorff 8 Dimension, hyperbolic set 59 Dimension, lower box 8 Dimension, lower pointwise 9 Dimension, pointwise 12 Dimension, repeller 41 Dimension, spectrum 82 102 108 210 211 Dimension, spectrum, hyperbolic set 93 Dimension, spectrum, repeller 81 Dimension, theory 7 19 24 Dimension, upper box 8 Dimension, upper pointwise 9 Distinguishing measure 130 131 138 entropy 14 15 Entropy, formula 106 Entropy, Kolmogorov - Sinai 14 Entropy, local 102 224 Entropy, spectrum 102 Entropy, spectrum, nonrigidity 193 Entropy, spectrum, rigidity 193 Entropy, topological 15 104 Equilibrium measure 15 Equivalence class 194 Equivalent function 194 Ergodic decomposition 226 Ergodic measure 13 Ergodic theory 7 13 Expanding map 41 Forward Lyapunov exponent 239 frequency 187 Full measure 110 Function, equivalent 194 Function, locally constant 188 194 Geometric construction 19 22 27 31 Geometric construction, nonstationary 31 35 Gibbs measure 25 Gibbs measure, product structure 55 Global stable manifold 211 Global unstable manifold 211 Hausdorff dimension 8 Hausdorff measure 7 Holonomy map along stable manifolds 59 Holonomy map along unstable manifolds 59 Hyperbolic Julia set 43 Hyperbolic measure 241 Hyperbolic set 49 Hyperbolic set, dimension spectrum 93 Hyperbolic set, locally maximal 50 Hyperbolicity, nonuniform 237 Invariant measure 13 Irregular set 130 160 Irregular set, local entropies 143 Irregular set, Lyapunov exponents 143 Irregular set, pointwise dimensions 143 Julia set 43 Julia set, hyperbolic 43 Kolmogorov - Sinai entropy 14 Limit set 22 Local entropy 102 224 Local entropy, formula 106 Local product structure 51 Local stable manifold 50 238 Local unstable manifold 50 238 Locally constant function 188 194 Locally maximal hyperbolic set 50 Lower 106 Lower box dimension 8 Lower pointwise dimension 9 Lower recurrence rate 255 Lower stable recurrence rate 272 Lower unstable recurrence rate 272 Lyapunov exponent, backward 240 Lyapunov exponent, forward 239 Map, coding 42 52 Map, conformal 43 59 Map, expanding 41 Map, shift 22 52 Markov chain, one-sided 42 Markov chain, two-sided 52 Markov partition 41 51 Markov partition, boundary 52 Measure, equilibrium 15 Measure, ergodic 13 Measure, full 110 Measure, full, dimension 70 Measure, Gibbs 25 Measure, Hausdorff 7 Measure, hyperbolic 241 Measure, invariant 13 Measure, maximal, 110 Measure, maximal, dimension 49 67 68 70 Mixed spectrum 103 Mixed spectrum, conditional variational principle 161 Moran cover 20 29 38 44 85 87 225 Multifractal analysis 101 Multifractal classification 191 Multifractal decomposition 81 101 160 Multifractal nonrigidity 206 Multifractal rigidity 191 197 Multifractal spectrum 101 Nonadditive thermodynamic formalism 31 Nonadditive topological pressure 34 Nondegenerate spectrum 179 Nonuniform hyperbolicity 237 Nonuniformly hyperbolic diffeomorphism 241 Nonuniformly hyperbolic trajectory 237 Number theory 186 Periodic point, repelling 43 Permutation automorphism 195 Pointwise dimension 12 106 108 Pointwise dimension, stable 243 Pointwise dimension, unstable 243 Polynomial, characteristic 206 Product structure 49 Product structure, Gibbs measure 55 Product structure, local 51 rectangle 51 224 230 Recurrence rate 255 Recurrence rate, lower 255 Recurrence rate, lower, stable 272 Recurrence rate, lower, unstable 272 Recurrence rate, stable 272 Recurrence rate, unstable 272 Recurrence rate, upper 255 Recurrence rate, upper, stable 272 Recurrence rate, upper, unstable 272 Repeller 41 Repeller, dimension spectrum 81 Repelling periodic point 43 Return time 255 Return time, stable 271 Return time, unstable 271 Rigidity, multifractal 191 197 Section 66 Separated set 14 Set, cylinder 24 Set, hyperbolic 49 Set, irregular 130 160 Set, irregular, local entropies 143 Set, irregular, Lyapunov exponents 143 Set, irregular, pointwise dimensions 143 Set, Julia 43 Set, limit 22 Set, separated 14 Shift map 22 52 Singular value 65 Solenoid 66 Specification 131 Spectrum, 108 Spectrum, degenerate 179 Spectrum, dimension 82 102 210 211 Spectrum, entropy 102 Spectrum, mixed 103 Spectrum, multifractal 101 Spectrum, nondegenerate 179 Stable boundary 52 Stable manifold, global 211 Stable manifold, local 50 238 Stable pointwise dimension 243 Stable recurrence rate 272 Stable return time 271 Symbolic dynamics 24 Thermodynamic formalism 7 14 24 Thermodynamic formalism, nonadditive 31 Topological entropy 15 104 Topological Markov chain, one-sided 42 Topological Markov chain, two-sided 52 Topological pressure 15 Topological pressure, nonadditive 34 Topological pressure, noncompact set 104 Topologically mixing 42 Transition matrix 42 52 Typical point 129 Unstable boundary 53 Unstable manifold, global 211 Unstable manifold, local 50 238 Unstable pointwise dimension 243 Unstable recurrence rate 272 Unstable return time 271 Upper 106 Upper box dimension 8 Upper pointwise dimension 9 Upper recurrence rate 255 Upper stable recurrence rate 272 Upper unstable recurrence rate 272 Variational Principle 147 Variational principle, conditional 147 155 167
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