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Devaney R.L. — An introduction to chaotic dynamical systems
Devaney R.L. — An introduction to chaotic dynamical systems

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Название: An introduction to chaotic dynamical systems

Автор: Devaney R.L.

Аннотация:

The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry, Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas. The first two chapters introduce the reader to a broad spectrum of fundamental topics in dynamics: hyperbolicity, symbolic dynamics, structural stability, stable and unstable manifolds and bifurcation theory. Readers familiar with linear algebra and complex analysis will be led to the brink of contemporary research in the books concluding chapter, but for anyone with a background in calculus, Devaney provides a comprehensive exploration into the mathematics of chaos.


Язык: en

Рубрика: Физика/Нелинейная динамика, Хаос/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1989

Количество страниц: 336

Добавлена в каталог: 16.08.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^1$-function      8
$C^r$-distance      54
Adding machine      137
Admissible sequence      144
Analytic map      261
Anosov map      190
Area preserving map      255
Asymptotic      19 185
Attracting fixed point      25 215 276
Attractor      25 201
Backward asymptotic      19 185
Baker map      39 52
Basin of attraction      280
Bifurcation      28 80
Bifurcation diagram      82
Bifurcation, Homoclinic      126
Bifurcation, period-doubling      82 90 310
Bifurcation, Saddle node      81 88 310
Block, L.      63
Branched manifold      209
Brouwer fixed point theorem      14
Bump function      8 17
Canonical family      109
Cantor bouquet      326
Cantor function      111
Cantor Middle-Fifths set      39
Cantor Middle-Thirds set      36 138
Cantor set      37 187 270
Cartesian product      171
Chain recurrence      232
Chain rule      10
Chaos      50 268
Closed set      14
Closing Lemma      116
Completely invariant      269
composition      10
Cone      238
Cone field      238
Continued fraction      307
Continuous dynamical system      3
Contraction mapping theorem      172
Core      238
Cover      61
Covering map      102
Critical point      10
DA map      212
Degenerate critical point      19
Degenerate homoclinic orbit      124
Dendrite      294
Denjoy map      108 112
Dense orbit      42
Dense set      15
Devil’s staircase      110
Diffeomorphism      9 170
Discrepancy      142
Discrete dynamical system      2
Douady, A.      260 316
double      67 137
Dynamical system      2
Eigenvalue      164
Eigenvector      164
Elliptic point      255
Elliptic transformation      267
Escape rate      314
Eventually periodic point      18
Exceptional point      274
Expanding attractor      208
Expansive      50
External ray      312
Fatou, P.      260
Fibonacci sequence      101
Filled in Julia set      311
First return map      75
Fixed point      18
Foliation      191
Forward asymptotic      19 185
Fractal      37
Full family      153
Fundamental domain      55
genealogy      154
Gradient like      231
Graph transform      226
Graphical analysis      20 32
Guckenheimer, J.      63
Hartman’s theorem      58
Henon attractor      211 213
Henon map      170 251
Heteroclinic point      122 188 233
Homeomorphism      9
Homoclinic bifurcation      125 257
Homoclinic orbit      123 188
Homoclinic point      122 194 233
Hopf bifurcation      242—244
Hopf bifurcation theorem      249
Horizontal curve      224
Horizontal line field      228
Hubbard, J.      260 316
Hyperbolic      24—28 214
Hyperbolic, fixed point      24 215
Hyperbolic, periodic point      24 21S
Hyperbolic, set      38 187 236
Hyperbolic, total automorphism      191
Hyperbolic, transformation      267
Implicit function theorem      10 171
Indifferent periodic point      276
Injective      9
integral      181
Intermediate Value Theorem      11
Inverse function theorem      172
Inverse limit      206
Involution      188 255
Irrational rotation      21
Iteration      2
Itinerary      44
Jacobi’s theorem      21
Jordan form      169
Julia set      269
Julia, G.      260
Kneading sequence      141
Kneading theory      140—143
Koenigs      276
Kupka — Smale theorem      117
Liapounov function      176
Lift      102
Limit point      14
Linear automorphism      230
Linear map      161
Linear structural stability      59
Local stable manifold      217
Local stable set      26
Local unstable manifold      217
Local unstable set      122
Lozi attractor      214
Mandelbrot set      295 299 311—317
Mandelbrot, B.      260
Mapping      17
Markov, partition      196
Matrix      161
Matrix representation      163
Maximum principle      263
Mean value theorem      10
Metric      40
Minimal set      136
Misiurewicz, M.      63 137 320
Mobius transformation      267
Montel’s theorem      274
Morse — Smale Map      59 114 235
Moser Twist Theorem      257
Moser, J.      276
Neutral periodic point      300
Non-degenerate critical point      19
Non-degenerate homoclinic orbit      124
Non-wandering      47
Normal family      272
Normal form      245
One-to-one      8
Onto      9
Open set      15
Orbit      17
Orbit diagram      134
Orbit, backward orbit      17
Orbit, forward orbit      17
Orbit, recurrent orbit      47 115
Orientation preserving      102
Palis, J.      235
Parabolic transformation      267
Perfect set      37
Period-doubling bifurcation      82 90 130 240 310
Periodic point      18
Periodic point, attracting      25
Periodic point, indifferent      276 300
Periodic point, neutral      300
Periodic point, repelling      26
Periodic point, weakly attracting      28
Periodic point, weakly repelling      27
Petal      302
Phase portrait      20
Plykin attractor      209
Pole      266
Quadratic map      31—39 268—272
Rational rotation      21
Recurrent point      47 116 232
Regular sequence      138
Renormalization      133 146
Repelling periodic point      26 215
Repellor      26
Reversible      255
Riemann sphere      265
Rotation number      103
Saddle node bifurcation      80 88 240 310
Sarkovskii order      62 256
Sarkovskii’s theorem      60 99
Schroder functional equation      277
Schwarz lemma      264
Schwarzian derivative      68—79 268
Sector bundle      223
Semi-conjugate      51
Sensitive dependence      49
Sequence space      40 184
Shift map      40 184 270
Siegel, C.L.      276 306
Simply connected      262
Sink      25 215
Smale horseshoe map      180
Smale, S.      93
Smooth function      8
Snap-back repellor      122
Solenoid      201
Source      26 215
Stable manifold      218 237
Stable set      19 185 269
Stable subspace      177
Standard family      109
Standard form      167
Steiner circle      268
Strange Attractor      211 258
Structural stability      53
Subshift of finite type      94 199
Sullivan, D.      260
Superattracting      276
Surjective      9
Symbolic dynamics      39—42 184 256
Tangent bifurcation      81
Tchebycheff polynomial      52
Tent map      38 52
Topological conjugacy      47
Topological transitivity      42 49
Torus      171 190
Totally disconnected      37
Trace      99
Transition family      153
Transition matrix      94
Transitive attractor      204
Transversality      233
Transverse homoclinic point      194
Trapping region      202
Uniformizing map      314
Unimodal map      130 140
Unstable manifold      218 237
Unstable set      19 186
Unstable subspace      177
Wandering interval      80 109
Weierstrass p function      296
Williams, R.      93 208
Young, L.-S.      63
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