| Preface |
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v | |
| Notation |
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ix | |
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1 | (16) |
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0.1 Definition and a (very brief) historical overview |
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1 | (2) |
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0.2 Continuous vs. discrete time |
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3 | (4) |
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0.3 The dynamical systems point of view |
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7 | (2) |
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9 | (8) |
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17 | (56) |
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1.1 Invariant and periodic points |
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17 | (6) |
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23 | (5) |
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28 | (5) |
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33 | (2) |
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1.5 Topological conjugacy and factor mappings |
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35 | (9) |
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1.6 Equicontinuity and weak mixing |
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44 | (13) |
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1.7 Miscellaneous examples |
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57 | (16) |
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2 Dynamical systems on the real line |
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73 | (44) |
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73 | (7) |
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2.2 Existence of periodic orbits |
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80 | (4) |
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2.3 The truncated tent map |
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84 | (3) |
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2.4 The double of a mapping |
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87 | (4) |
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2.5 The Markov graph of a periodic orbit in an interval |
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91 | (10) |
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2.6 Transitivity of mappings of an interval |
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101 | (16) |
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117 | (48) |
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3.1 Limit sets and attraction |
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117 | (9) |
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126 | (6) |
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3.3 Stability and attraction for periodic orbits |
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132 | (11) |
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3.4 Asymptotic stability in locally compact spaces |
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143 | (10) |
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3.5 The structure of (asymptotically) stable sets |
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153 | (12) |
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165 | (53) |
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165 | (4) |
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4.2 Almost periodic points and minimal orbit closures |
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169 | (6) |
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175 | (7) |
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182 | (15) |
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4.5 Asymptotic stability and basic sets |
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197 | (21) |
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218 | (64) |
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5.1 Notation and terminology |
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218 | (5) |
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223 | (3) |
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226 | (10) |
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236 | (8) |
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244 | (9) |
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5.6 Recurrence, almost periodicity and mixing |
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253 | (29) |
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6 Symbolic representations |
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282 | (43) |
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6.1 Topological partitions |
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282 | (11) |
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293 | (9) |
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302 | (23) |
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325 | (53) |
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325 | (11) |
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7.2 Chaos(1): sensitive systems |
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336 | (6) |
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7.3 Chaos(2): scrambled sets |
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342 | (13) |
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7.4 Horseshoes for interval maps |
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355 | (10) |
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7.5 Existence of a horseshoe |
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365 | (13) |
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378 | (45) |
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378 | (9) |
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8.2 Independence of the metric; factor maps |
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387 | (4) |
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8.3 Maps on intervals and circles |
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391 | (3) |
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8.4 The definition with covers |
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394 | (8) |
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8.5 Miscellaneous results |
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402 | (4) |
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8.6 Positive entropy and horseshoes for interval maps |
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406 | (17) |
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423 | (30) |
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423 | (3) |
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426 | (2) |
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428 | (2) |
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430 | (2) |
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A.5 Subspaces, products and quotients |
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432 | (2) |
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434 | (3) |
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437 | (7) |
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444 | (2) |
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446 | (3) |
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A.10 Miscellaneous results |
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449 | (4) |
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453 | (12) |
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453 | (3) |
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B.2 Proof of Brouwer's Theorem |
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456 | (5) |
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461 | (4) |
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465 | (16) |
| Literature |
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481 | (4) |
| Index |
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485 | |
