| Preface to the English Edition |
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| Preface to the Chinese Edition |
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Certain Ergodic Properties of a Differential System on a Compact Differentiable Manifold |
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1 | (55) |
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One-parameter Transformation Groups on Frame Bundles |
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2 | (4) |
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Covariant Differentiation, the Function ωκ(α) |
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6 | (5) |
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11 | (4) |
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15 | (11) |
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On the Determination of the Style Number |
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26 | (9) |
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Comparison of Certain Functions |
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35 | (9) |
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3-dimensional Systems with Degenerate Style Numbers |
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44 | (5) |
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Square Matrix Rα(t) and Divergence divS |
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49 | (7) |
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55 | (1) |
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Standard Systems of Differential Equations |
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56 | (80) |
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A Review of Standard Systems of Differential Equations |
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58 | (11) |
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Another Class of Standard Systems of Differential Equations |
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69 | (30) |
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Families Mp of Differential Equations |
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99 | (20) |
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119 | (17) |
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135 | (1) |
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Obstruction Sets and Strong Transversality Condition |
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136 | (10) |
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136 | (2) |
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The Obstruction Set Ob(S) |
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138 | (1) |
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139 | (4) |
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143 | (3) |
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145 | (1) |
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146 | (58) |
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148 | (11) |
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159 | (6) |
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165 | (6) |
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Linear Theory of Normal Sets |
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171 | (18) |
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Linear Theory of Normal Sets (continued) |
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189 | (15) |
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203 | (1) |
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On the Stability Conjecture |
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204 | (25) |
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Introduction and Statements of the Main Results |
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204 | (1) |
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The Class χ* (Mn) of Vector Fields |
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205 | (2) |
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Contractible Periodic Orbits |
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207 | (4) |
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The Case S &epsis; χ* (M3) |
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211 | (6) |
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The ``Sifting'' Lemma and the Proof of Theorem 5.4.1 |
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217 | (7) |
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Proofs of Theorems 5.1.1 and 5.1.2 |
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224 | (5) |
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226 | (1) |
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227 | (2) |
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229 | (51) |
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229 | (2) |
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Obstruction Sets and Minimal Rambling Sets |
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231 | (4) |
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Simply Minimal Rambling Sets |
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235 | (8) |
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The Set M(η, T; p) and the Hunched Set R(ζ,p) U L(ζ,p) of S &epsis; χ* |
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243 | (13) |
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Non-Simply Minimal Rambling Sets of S &epsis; χ* and Proofs of Theorem 6.1.1 and 6.1.2 |
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256 | (18) |
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On the Sets R(ζ,p) and L(ζ,p) |
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274 | (6) |
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278 | (2) |
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Standard Systems of Differential Equations and Obstruction Sets with Applications to Structural Stability Problems |
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280 | (25) |
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Global Linearization of Differential Systems and Expression by Linear Systems |
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280 | (3) |
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Standard Systems of Equations |
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283 | (2) |
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A Reduction to Lower Dimension by 1 |
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285 | (4) |
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289 | (3) |
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The Family χ* of Differential Systems |
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292 | (2) |
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294 | (3) |
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Simple and Non-Simple Minimal Rambling Sets |
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297 | (2) |
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Ω-Stability and Structural Stability |
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299 | (6) |
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302 | (3) |
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On Characterizations of Structural Stability |
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305 | (6) |
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305 | (1) |
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Preliminaries. Obstruction Sets and Minimal Rambling Sets |
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306 | (1) |
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307 | (2) |
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309 | (2) |
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310 | (1) |
| Appendix to the Chinese Edition |
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311 | (11) |
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320 | (1) |
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Supplement (October 1990) |
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321 | (1) |
| Appendix A An Extension of the C1 Closing Lemma |
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322 | (51) |
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322 | (2) |
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A.2 An Abstract of the Proof |
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324 | (3) |
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327 | (2) |
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A.4 The Family of Squared Matrices &thetas;(t) (0 ≤ t < ∞) |
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329 | (7) |
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A.5 The Proof of Theorem I |
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336 | (3) |
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A.6 The Proof of Theorem II |
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339 | (15) |
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A.7 Standard Systems of Differential Equations |
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354 | (3) |
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A.8 The Proof of the Main Theorem |
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357 | (13) |
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A.9 The Case that ωa U αa is Non-empty |
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370 | (3) |
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371 | (2) |
| Appendix B Obstruction Sets, Minimal Rambling Sets and Their Applications |
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373 | (12) |
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373 | (1) |
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B.2 Relations between Obstruction Sets and Transversality Conditions |
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374 | (2) |
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B.3 A Filtration for Normal Sets |
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376 | (1) |
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B.4 Minimal Rambling Sets |
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377 | (1) |
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B.5 The Families χ** (Mn) and χ⊗ (Mn) |
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378 | (2) |
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B.6 On Stability of Differential Systems |
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380 | (5) |
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382 | (3) |
| Editor's Postscripts |
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385 | |
