A first course in dynamics: with a panorama of recent developments
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Pr.
2003
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Publisher description Table of contents Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke. |
| Physical Description: | X, 424 S. graph. Darst. |
| ISBN: | 0521583047 0521587506 9780521583046 9780521587501 |
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MARC
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| 100 | 1 | |a Hasselblatt, Boris |d 1961- |e Verfasser |0 (DE-588)137987471 |4 aut | |
| 245 | 1 | 0 | |a A first course in dynamics |b with a panorama of recent developments |c Boris Hasselblatt ; Anatole Katok |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Pr. |c 2003 | |
| 300 | |a X, 424 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke. | ||
| 650 | 7 | |a Differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Dynamique différentiable | |
| 650 | 7 | |a Dynamische systemen |2 gtt | |
| 650 | 7 | |a Niet-lineaire vergelijkingen |2 gtt | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 0 | 7 | |a Differenzierbares dynamisches System |0 (DE-588)4137931-7 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
Preface page x
1 Introduction 1
1.1 Dynamics 1
1.2 Dynamics in Nature 4
1.3 Dynamics in Mathematics 19
PART 1. A COURSE IN DYNAMICS: FROM SIMPLE TO
COMPLICATED BEHAVIOR 29
2 Systems with Stable Asymptotic Behavior 31
2.1 Linear Maps and Linearization 31
2.2 Contractions in Euclidean Space 32
2.3 Nondecreasing Maps of an Interval and Bifurcations 45
2.4 Differential Equations 49
2.5 Quadratic Maps 57
2.6 Metric Spaces 61
2.7 Fractals 69
3 Linear Maps and Linear Differential Equations 73
3.1 Linear Maps in the Plane 73
3.2 Linear Differential Equations in the Plane 86
3.3 Linear Maps and Differential Equations in Higher Dimension 90
4 Recurrence and Equidistribution on the Circle 96
4.1 Rotations of the Circle 96
4.2 Some Applications of Density and Uniform Distribution 109
4.3 Invertible Circle Maps 123
4.4 Cantor Phenomena 135
5 Recurrence and Equidistribution in Higher Dimension 143
5.1 Translations and Linear Flows on the Torus 143
5.2 Applications of Translations and Linear Flows 152
v
vi Contents
6 Conservative Systems 155
6.1 Preservation of Phase Volume and Recurrence 155
6.2 Newtonian Systems of Classical Mechanics 162
6.3 Billiards: Definition and Examples 177
6.4 Convex Billiards 186
7 Simple Systems with Complicated Orbit Structure 196
7.1 Growth of Periodic Points 196
7.2 Topological Transitivity and Chaos 205
7.3 Coding 211
7.4 More Examples of Coding 221
7.5 Uniform Distribution 229
7.6 Independence, Entropy, Mixing 235
8 Entropy and Chaos 242
8.1 Dimension of a Compact Space 242
8.2 Topological Entropy 245
8.3 Applications and Extensions 251
PART 2. PANORAMA OF DYNAMICAL SYSTEMS 257
9 Simple Dynamics as a Tool 259
9.1 Introduction 259
9.2 Implicit and Inverse Function Theorems in Euclidean Space 260
9.3 Persistence of Transverse Fixed Points 265
9.4 Solutions of Differential Equations 267
9.5 Hyperbolicity 273
10 Hyperbolic Dynamics 279
10.1 Hyperbolic Sets 279
10.2 Orbit Structure and Orbit Growth 284
10.3 Coding and Mixing 291
10.4 Statistical Properties 294
10.5 Nonuniformly Hyperbolic Dynamical Systems 298
11 Quadratic Maps 299
11.1 Preliminaries 299
11.2 Development of Simple Behavior Beyond the First Bifurcation 303
11.3 Onset of Complexity 307
11.4 Hyperbolic and Stochastic Behavior 314
12 Homoclinic Tangles 318
12.1 Nonlinear Horseshoes 318
12.2 Homoclinic Points 320
12.3 The Appearance of Horseshoes 322
12.4 The Importance of Horseshoes 324
12.5 Detecting Homoclinic Tangles: The Poincare Melnikov
Method 327
12.6 Homoclinic Tangencies 328
Contents vii
13 Strange Attractors 331
13.1 Familiar Attractors 331
13.2 The Solenoid 333
13.3 TheLorenzAttractor 335
14 Variational Methods, IWist Maps, and Closed Geodesies 342
14.1 The Variational Method and Birkhoff Periodic Orbits
for Billiards 342
14.2 Birkhoff Periodic Orbits and Aubry Mather Theory
for Twist Maps 346
14.3 Invariant Circles and Regions of Instability 357
14.4 Periodic Points for Maps of the Cylinder 360
14.5 Geodesies on the Sphere 362
15 Dynamics, Number Theory, and Diophantine Approximation 365
15.1 Uniform Distribution of the Fractional Parts of Polynomials 365
15.2 Continued Fractions and Rational Approximation 369
15.3 The Gaufi Map 374
15.4 Homogeneous Dynamics, Geometry, and Number Theory 377
15.5 Quadratic Forms in Three Variables 383
Reading 386
APPENDIX 389
A. 1 Metric Spaces 389
A.2 Differentiability 400
A.3 Riemann Integration in Metric Spaces 401
Hints and Answers 408
Solutions 414
Index 419
|
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| id | DE-604.BV014639406 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:36Z |
| institution | BVB |
| isbn | 0521583047 0521587506 9780521583046 9780521587501 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009942380 |
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| spelling | Hasselblatt, Boris 1961- Verfasser (DE-588)137987471 aut A first course in dynamics with a panorama of recent developments Boris Hasselblatt ; Anatole Katok 1. publ. Cambridge [u.a.] Cambridge Univ. Pr. 2003 X, 424 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke. Differentiaalvergelijkingen gtt Dynamique différentiable Dynamische systemen gtt Niet-lineaire vergelijkingen gtt Differentiable dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s DE-604 Katok, Anatole 1944-2018 Sonstige (DE-588)111187125 oth http://www.loc.gov/catdir/description/cam022/2002019246.html Publisher description http://www.loc.gov/catdir/toc/cam022/2002019246.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009942380&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hasselblatt, Boris 1961- A first course in dynamics with a panorama of recent developments Differentiaalvergelijkingen gtt Dynamique différentiable Dynamische systemen gtt Niet-lineaire vergelijkingen gtt Differentiable dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4137931-7 |
| title | A first course in dynamics with a panorama of recent developments |
| title_auth | A first course in dynamics with a panorama of recent developments |
| title_exact_search | A first course in dynamics with a panorama of recent developments |
| title_full | A first course in dynamics with a panorama of recent developments Boris Hasselblatt ; Anatole Katok |
| title_fullStr | A first course in dynamics with a panorama of recent developments Boris Hasselblatt ; Anatole Katok |
| title_full_unstemmed | A first course in dynamics with a panorama of recent developments Boris Hasselblatt ; Anatole Katok |
| title_short | A first course in dynamics |
| title_sort | a first course in dynamics with a panorama of recent developments |
| title_sub | with a panorama of recent developments |
| topic | Differentiaalvergelijkingen gtt Dynamique différentiable Dynamische systemen gtt Niet-lineaire vergelijkingen gtt Differentiable dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Differentiaalvergelijkingen Dynamique différentiable Dynamische systemen Niet-lineaire vergelijkingen Differentiable dynamical systems Differenzierbares dynamisches System |
| url | http://www.loc.gov/catdir/description/cam022/2002019246.html http://www.loc.gov/catdir/toc/cam022/2002019246.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009942380&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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