Bifurcations and Catastrophes: Geometry of Solutions to Nonlinear ProblemsSpringer Science & Business Media, 15 déc. 1999 - 304 pages Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential mathematical structures. Taking a unified view, it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments. |
Table des matières
II | 13 |
III | 14 |
IV | 17 |
V | 19 |
VI | 20 |
VII | 24 |
VIII | 26 |
IX | 29 |
LIX | 157 |
LX | 159 |
LXI | 161 |
LXII | 164 |
LXIII | 168 |
LXIV | 170 |
LXV | 172 |
LXVI | 175 |
X | 31 |
XI | 32 |
XII | 36 |
XIII | 40 |
XIV | 43 |
XV | 45 |
XVI | 47 |
XVII | 50 |
XVIII | 52 |
XIX | 55 |
XX | 58 |
XXI | 60 |
XXII | 63 |
XXIII | 65 |
XXIV | 69 |
XXV | 70 |
XXVI | 74 |
XXVII | 75 |
XXVIII | 78 |
XXIX | 81 |
XXX | 83 |
XXXI | 86 |
XXXII | 87 |
XXXIII | 88 |
XXXIV | 90 |
XXXV | 93 |
XXXVI | 96 |
XXXVII | 98 |
XXXVIII | 100 |
XXXIX | 104 |
XL | 108 |
XLI | 109 |
XLII | 111 |
XLIII | 115 |
XLIV | 117 |
XLV | 119 |
XLVI | 120 |
XLVII | 123 |
XLVIII | 126 |
XLIX | 130 |
L | 133 |
LI | 135 |
LII | 138 |
LIII | 140 |
LIV | 143 |
LV | 147 |
LVI | 149 |
LVII | 151 |
LVIII | 155 |
LXVII | 179 |
LXVIII | 181 |
LXIX | 185 |
LXX | 188 |
LXXI | 191 |
LXXII | 193 |
LXXIII | 196 |
LXXIV | 200 |
LXXV | 203 |
LXXVI | 206 |
LXXVII | 211 |
LXXVIII | 213 |
LXXIX | 219 |
LXXX | 220 |
LXXXI | 223 |
LXXXII | 226 |
LXXXIII | 228 |
LXXXIV | 230 |
LXXXV | 233 |
LXXXVI | 234 |
LXXXVII | 238 |
LXXXVIII | 239 |
LXXXIX | 242 |
XC | 243 |
XCI | 247 |
XCII | 249 |
XCIII | 250 |
XCIV | 252 |
XCV | 254 |
XCVI | 256 |
XCVII | 258 |
XCVIII | 260 |
XCIX | 264 |
C | 266 |
CI | 268 |
CII | 269 |
CIII | 270 |
CIV | 273 |
CV | 275 |
CVI | 277 |
CVII | 280 |
CVIII | 282 |
CX | 284 |
CXI | 287 |
CXII | 289 |
293 | |
295 | |
CXV | |
Autres éditions - Tout afficher
Expressions et termes fréquents
belongs bifurcation bijective centre closed orbits codimension compact condition consider containing coordinates Corollary countable critical point cusp points deduce defined definition deformation denote dense set dense subset diffeomorphism differential equation dim(E dim(F dimension eigenvalues element embedding End(E endomorphism example exists an open exp(tu exponential fact finite finite-dimensional vector space germ Hence Hessian form homeomorphism hyperbolic immersion implies injective integral curve integral flow intersection invariant inverse Lemma linear map local diffeomorphism manifold matrix neighbourhood nondegenerate nonzero norm notation obtain open dense open set open subset orbitally equivalent parameters partial derivatives particular periodic orbit phase portrait phase space Poincaré map polynomial proof properties Proposition prove residual subset restriction scalar Sect sequence singular point Sp(u structurally stable submanifold subspace sufficiently close Suppose surjective tangent space topologically conjugate Transversality Theorem variables zero