Introduction to the Modern Theory of Dynamical SystemsCambridge University Press, 1995 - 802 pages This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. |
Table des matières
vii | |
II | xiii |
III | 1 |
IV | 6 |
V | 8 |
VI | 10 |
VII | 13 |
VIII | 15 |
LXXIX | 405 |
LXXX | 410 |
LXXXI | 412 |
LXXXII | 415 |
LXXXIII | 419 |
LXXXIV | 423 |
LXXXV | 424 |
LXXXVI | 425 |
IX | 19 |
X | 26 |
XI | 28 |
XII | 32 |
XIII | 35 |
XIV | 39 |
XV | 42 |
XVI | 47 |
XVII | 57 |
XIX | 64 |
XX | 68 |
XXI | 71 |
XXII | 79 |
XXIII | 87 |
XXIV | 90 |
XXV | 94 |
XXVI | 100 |
XXVII | 105 |
XXIX | 119 |
XXX | 128 |
XXXI | 133 |
XXXIII | 146 |
XXXIV | 161 |
XXXV | 173 |
XXXVI | 179 |
XXXVII | 183 |
XXXVIII | 196 |
XXXIX | 200 |
XL | 205 |
XLI | 219 |
XLII | 229 |
XLIII | 233 |
XLIV | 235 |
XLV | 237 |
XLVII | 239 |
XLVIII | 260 |
XLIX | 263 |
L | 273 |
LI | 278 |
LII | 287 |
LIV | 290 |
LV | 298 |
LVI | 304 |
LVII | 307 |
LVIII | 308 |
LIX | 310 |
LX | 316 |
LXI | 318 |
LXII | 323 |
LXIII | 326 |
LXIV | 330 |
LXV | 335 |
LXVI | 336 |
LXVII | 339 |
LXVIII | 349 |
LXIX | 365 |
LXX | 367 |
LXXI | 372 |
LXXII | 376 |
LXXIII | 379 |
LXXIV | 381 |
LXXV | 387 |
LXXVI | 393 |
LXXVII | 401 |
LXXVIII | 403 |
LXXXVII | 434 |
LXXXVIII | 441 |
LXXXIX | 447 |
XC | 451 |
XCI | 452 |
XCII | 457 |
XCIII | 460 |
XCIV | 464 |
XCV | 470 |
XCVI | 479 |
XCVII | 483 |
XCVIII | 489 |
XCIX | 493 |
C | 500 |
CI | 505 |
CII | 511 |
CIII | 514 |
CIV | 519 |
CV | 520 |
CVI | 525 |
CVII | 526 |
CVIII | 529 |
CIX | 531 |
CX | 532 |
CXI | 537 |
CXII | 541 |
CXIII | 549 |
CXIV | 551 |
CXV | 555 |
CXVI | 559 |
CXVII | 565 |
CXVIII | 571 |
CXIX | 574 |
CXX | 581 |
CXXI | 583 |
CXXII | 587 |
CXXIII | 591 |
CXXIV | 597 |
CXXV | 608 |
CXXVI | 615 |
CXXVII | 623 |
CXXVIII | 628 |
CXXIX | 637 |
CXXX | 643 |
CXXXI | 651 |
CXXXII | 657 |
CXXXIII | 659 |
CXXXIV | 660 |
CXXXV | 672 |
CXXXVI | 678 |
CXXXVII | 693 |
CXXXVIII | 701 |
CXXXIX | 703 |
CXL | 711 |
CXLI | 715 |
CXLII | 727 |
CXLIII | 730 |
CXLIV | 731 |
CXLV | 735 |
CXLVI | 738 |
CXLVII | 741 |
CXLVIII | 765 |
781 | |
793 | |
Expressions et termes fréquents
Anosov Anosov diffeomorphism asymptotic automorphism behavior called circle closed compact component conjugacy consider construction contains continuous map converges coordinates Corollary critical points curve defined Definition denote dense diffeomorphism differentiable disjoint dynamical systems eigenvalues endpoints equation equivalent ergodic theory example Exercise exists expanding maps exponential f-invariant finite fixed point follows function geodesic flow global graph Hamiltonian hence Hölder continuous homeomorphism homotopy htop f hyperbolic set implies integrable intersection invariant measure iterates Lebesgue measure Lemma Let f linear map locally maximal map f matrix metric space minimal neighborhood obtain open set orbit segment partition periodic points Poincaré preimages preserves proof of Theorem Proposition Prove rotation number Section semiconjugacy sequence smooth stable and unstable subset symplectic tangent topological entropy topological Markov chain topologically conjugate topologically mixing topologically transitive torus transformation transverse twist map unique unstable manifolds vector field zero