| Preface | p. xiii |
| Introduction | p. 1 |
| Dimension and recurrence in hyperbolic dynamics | p. 1 |
| Contents of the book: a brief tour | p. 3 |
| Basic Notions | p. 7 |
| Dimension theory | p. 7 |
| Ergodic theory | p. 13 |
| Thermodynamic formalism | p. 14 |
| Dimension Theory | p. 17 |
| Dimension Theory and Thermodynamic Formalism | p. 19 |
| Dimension theory of geometric constructions | p. 19 |
| Thermodynamic formalism and dimension theory | p. 24 |
| Thermodynamic formalism for symbolic dynamics | p. 24 |
| Dimension of limit sets of geometric constructions | p. 27 |
| Nonstationary geometric constructions | p. 31 |
| Nonadditive thermodynamic formalism | p. 31 |
| Dimension of limit sets of nonstationary constructions | p. 35 |
| Repellers and Hyperbolic Sets | p. 41 |
| Dimension of repellers of conformal maps | p. 41 |
| Hyperbolic sets and Markov partitions | p. 49 |
| Basic notions and product structure | p. 49 |
| Boundaries of Markov partitions | p. 52 |
| Product structure of Gibbs measures | p. 55 |
| Dimension of hyperbolic sets of conformal maps | p. 59 |
| Dimension for nonconformal maps: brief notes | p. 64 |
| Measures of Maximal Dimension | p. 67 |
| Basic notions and basic properties | p. 67 |
| Existence of measures of maximal dimension | p. 70 |
| Multifractal Analysis: Core Theory | p. 79 |
| Multifractal Analysis of Equilibrium Measures | p. 81 |
| Dimension spectrum for repellers | p. 81 |
| Dimension spectrum for hyperbolic sets | p. 93 |
| General Concept of Multifractal Analysis | p. 101 |
| General concept and basic notions | p. 101 |
| The notion of u-dimension | p. 103 |
| Multifractal analysis of u-dimension | p. 108 |
| Domain of the spectra | p. 111 |
| Existence of spectra with prescribed data | p. 113 |
| Nondegeneracy of the spectra | p. 120 |
| Dimension of Irregular Sets | p. 127 |
| Introduction | p. 127 |
| Irregular sets and distinguishing measures | p. 130 |
| Existence of distinguishing measures | p. 138 |
| Topological Markov chains | p. 139 |
| Repellers | p. 141 |
| Hyperbolic sets | p. 144 |
| Variational Principles in Multifractal Analysis | p. 147 |
| Conditional variational principle | p. 147 |
| Topological Markov chains | p. 156 |
| Dimension of irregular sets | p. 160 |
| Repellers and mixed spectra | p. 161 |
| Multifractal Analysis: Further Developments | p. 165 |
| Multidimensional Spectra and Number Theory | p. 167 |
| Conditional variational principle | p. 167 |
| Geometry of the domains | p. 173 |
| Regularity of the multifractal spectra | p. 177 |
| New phenomena in multidimensional spectra | p. 179 |
| Topological Markov chains | p. 182 |
| Finer structure of the spectrum | p. 184 |
| Applications to number theory | p. 186 |
| Multifractal Rigidity | p. 191 |
| Multifractal classification of dynamical systems | p. 191 |
| Entropy spectrum and topological Markov chains | p. 193 |
| Equivalence classes of functions | p. 193 |
| Locally constant functions | p. 194 |
| Multifractal rigidity for locally constant functions | p. 197 |
| Failure of multifractal rigidity | p. 206 |
| Hyperbolic Sets: Past and Future | p. 209 |
| A model case: the Smale horseshoe | p. 209 |
| Dimension spectra | p. 210 |
| Existence of full measures | p. 213 |
| Formula for the spectrum | p. 219 |
| Conditional variational principle | p. 220 |
| Hyperbolicity and Recurrence | p. 221 |
| Pointwise Dimension for Hyperbolic Dynamics | p. 223 |
| Repellers of conformal maps | p. 223 |
| Formula for the pointwise dimension | p. 223 |
| Dimension along ergodic decompositions | p. 228 |
| Hyperbolic sets of conformal maps | p. 230 |
| Formula for the pointwise dimension | p. 230 |
| Dimension along ergodic decompositions | p. 234 |
| Product Structure of Hyperbolic Measures | p. 237 |
| Nonuniform hyperbolicity | p. 237 |
| Dynamical systems with nonzero Lyapunov exponents | p. 239 |
| Product structure of hyperbolic measures | p. 241 |
| Product structure of measures in hyperbolic sets | p. 244 |
| Quantitative Recurrence and Dimension Theory | p. 255 |
| Basic notions | p. 255 |
| Upper bounds for recurrence rates | p. 256 |
| Recurrence rate and pointwise dimension | p. 261 |
| Product structure and recurrence | p. 264 |
| Preliminary results | p. 264 |
| Stable and unstable recurrence rates | p. 271 |
| Product structure of recurrence | p. 281 |
| Bibliography | p. 285 |
| Index | p. 297 |
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