Invitation to dynamical systems:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Upper Saddle River, NJ
Prentice-Hall
1996
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007549616&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVII, 373 S. Ill., graph. Darst. |
| ISBN: | 0131850008 |
Internformat
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| 100 | 1 | |a Scheinerman, Edward R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Invitation to dynamical systems |c Edward R. Scheinerman |
| 264 | 1 | |a Upper Saddle River, NJ |b Prentice-Hall |c 1996 | |
| 300 | |a XVII, 373 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Dynamique différentiable |2 ram | |
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Datensatz im Suchindex
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| DE-BY-TUM_media_number | 040001912536 |
| _version_ | 1826435158234890240 |
| adam_text | DYNAMICAL SYSTEMS EDWARD R. SCHEINERMAN DEPARTMENT OF MATHEMATICAL
SCIENCES THE JOHNS HOPKINS UNIVERSITY PRENTICE HALL UPPER SADDLE RIVER,
NEW JERSEY 07458 PREFACE XI 1 INTRODUCTION 1 1.1 WHAT IS A DYNAMICAL
SYSTEM? 1 1.1.1 STATE VECTORS 1 1.1.2 THE NEXT INSTANT: DISCRETE TIME 2
1.1.3 THE NEXT INSTANT: CONTINUOUS TIME 4 1.1.4 SUMMARY 6 PROBLEMS . _ 6
1.2 EXAMPLES 8 1.2.1 MASS AND SPRING 8 1.2.2 RLC CIRCUITS 10 1.2.3
PENDULUM 11 1.2.4 YOUR BANK ACCOUNT 16 1.2.5 ECONOMIC GROWTH 17 1.2.6
PUSHING BUTTONS ON YOUR CALCULATOR 19 1.2.7 MICROBES 22 1.2.8 PREDATOR
AND PREY 24 1.2.9 NEWTON S METHOD 26 1.2.10 EULER S METHOD 28 1.2.11
RANDOM NUMBER GENERATION 31 PROBLEMS 32 1.3 WHAT WE WANT; WHAT WE CAN
GET 35 2 LINEAR SYSTEMS 37 2.1 ONE DIMENSION 37 VI CONTENTS 2.1.1
DISCRETE TIME 37 2.1.2 CONTINUOUS TIME 45 2.1.3 SUMMARY 48 PROBLEMS 49
2.2 TWO (AND MORE) DIMENSIONS 50 2.2.1 DISCRETE TIME 51 2.2.2 CONTINUOUS
TIME 57 2.2.3 THE NONDIAGONALIZABLE CASE* 81 PROBLEMS 88 2.3
EXAMPLIFICATION: MARKOV CHAINS 91 2.3.1 INTRODUCTION 91 2.3.2 MARKOV
CHAINS AS LINEAR SYSTEMS 93 2.3.3 THE LONG TERM 96 PROBLEMS 98 3
NONLINEAR SYSTEMS 1: FIXED POINTS 101 3.1 FIXED POINTS 102 3.1.1 WHAT IS
A FIXED POINT? 102 3.1.2 FINDING FIXED POINTS 103 3.1.3 STABILITY 104
PROBLEMS 108 3.2 LINEARIZATION 110 3.2.1 ONE DIMENSION 110 3.2.2 TWO AND
MORE DIMENSIONS 117 PROBLEMS 126 3.3 LYAPUNOV FUNCTIONS 128 3.3.1
LINEARIZATION CAN FAIL 128 3.3.2 ENERGY 130 3.3.3 LYAPUNOV S METHOD 133
3.3.4 GRADIENT SYSTEMS 137 PROBLEMS 144 3.4 EXAMPLIFICATION: ITERATIVE
METHODS FOR SOLVING EQUATIONS . 146 PROBLEMS 150 4 NONLINEAR SYSTEMS 2:
PERIODICITY AND CHAOS 153 4.1 CONTINUOUS TIME 154 4.1.1 ONE DIMENSION:
NO PERIODICITY 154 4.1.2 TWO DIMENSIONS: THE POINCARE-BENDIXSON THEOREM
155 CONTENTS VII 4.1.3 THE HOPF BIFURCATION* 161 4.1.4 HIGHER
DIMENSIONS: THE LORENZ SYSTEM AND CHAOS . 163 PROBLEMS 167 4.2 DISCRETE
TIME . . . . 168 4.2.1 PERIODICITY 169 4.2.2 STABILITY OF PERIODIC
POINTS 173 4.2.3 BIFURCATION 175 4.2.4 SARKOVSKII S THEOREM* 188 4.2.5
CHAOS AND SYMBOLIC DYNAMICS 202 PROBLEMS 216 4.3 EXAMPLIFICATION: RIFFLE
SHUFFLES AND THE SHIFT MAP 218 4.3.1 RIFFLE SHUFFLES 218 4.3.2 THE SHIFT
MAP 219 4.3.3 SHIFTING AND SHUFFLING 223 4.3.4 SHUFFLING AGAIN AND AGAIN
226 PROBLEMS 229 5 FRACTALS 231 5.1 CANTOR S SET 231 5.1.1 SYMBOLIC
REPRESENTATION OF CANTOR S SET 232 5.1.2 CANTOR S SET IN CONVENTIONAL
NOTATION 233 5.1.3 THE LINK BETWEEN THE TWO REPRESENTATIONS 236 5.1.4
TOPOLOGICAL PROPERTIES OF THE CANTOR SET 236 5.1.5 IN WHAT SENSE A
FRACTAL? 240 PROBLEMS 241 5.2 BITING OUT THE MIDDLE IN THE PLANE 242
5.2.1 SIERPIRISKI S TRIANGLE 242 5.2.2 KOCH S SNOWFLAKE 243 PROBLEMS 245
5.3 CONTRACTION MAPPING THEOREMS 246 5.3.1 CONTRACTION MAPS 246 5.3.2
CONTRACTION MAPPING THEOREM ON THE REAL LINE . . . 247 5.3.3 CONTRACTION
MAPPING IN HIGHER DIMENSIONS . . . . 249 5.3.4 CONTRACTIVE AFFINE MAPS:
THE SPECTRAL NORM* . . . . 250 5.3.5 OTHER METRIC SPACES 254 5.3.6
COMPACT SETS AND HAUSDORFF DISTANCE 255 PROBLEMS 258 5.4 ITERATED
FUNCTION SYSTEMS 260 5.4.1 FROM POINT MAPS TO SET MAPS 260 VIII CONTENTS
5.4.2 THE UNION OF SET MAPS 262 5.4.3 EXAMPLES REVISITED 265 5.4.4 IFSS
DEFINED 270 5.4.5 WORKING BACKWARD 271 PROBLEMS 276 5.5 ALGORITHMS FOR
DRAWING FRACTALS 276 5.5.1 A DETERMINISTIC ALGORITHM 277 5.5.2 DANCING
ON FRACTALS 279 5.5.3 A RANDOMIZED ALGORITHM 283 PROBLEMS 286 5.6
FRACTAL DIMENSION 287 5.6.1 COVERING WITH BALLS 287 5.6.2 DEFINITION OF
DIMENSION 290 5.6.3 SIMPLIFYING THE DEFINITION 292 5.6.4 JUST-TOUCHING
SIMILITUDES AND DIMENSION 300 PROBLEMS 306 5.7 EXAMPLIFICATION: FRACTALS
IN NATURE 307 5.7.1 DIMENSION OF PHYSICAL FRACTALS 308 5.7.2 ESTIMATING
SURFACE AREA 312 5.7.3 IMAGE ANALYSIS 314 PROBLEMS 314 6 COMPLEX
DYNAMICAL SYSTEMS 317 6.1 JULIA SETS 317 6.1.1 DEFINITION AND EXAMPLES
317 6.1.2 ESCAPE-TIME ALGORITHM 324 6.1.3 OTHER JULIA SETS 326 PROBLEMS
327 6.2 THE MANDELBROT SET 327 6.2.1 DEFINITION AND VARIOUS VIEWS 327
6.2.2 ESCAPE-TIME ALGORITHM 332 PROBLEMS 332 6.3 EXAMPLIFICATION:
NEWTON S METHOD REVISITED 333 PROBLEMS 336 6.4 EXAMPLIFICATION: COMPLEX
BASES 336 6.4.1 PLACE VALUE REVISITED 336 6.4.2 IFSS REVISITED 338
PROBLEMS 340 CONTENTS IX A BACKGROUND MATERIAL 341 A.I LINEAR ALGEBRA
341 A. 1.1 MUCH ADO ABOUT 0 341 A.1.2 LINEAR INDEPENDENCE 342 A. 1.3
EIGENVALUES/VECTORS 342 A. 1.4 DIAGONALIZATION 343 A.1.5 JORDAN
CANONICAL FORM* 343 A. 1.6 BASIC LINEAR TRANSFORMATIONS OF THE PLANE 344
A.2 COMPLEX NUMBERS 347 A.3 CALCULUS 349 A.3.1 INTERMEDIATE AND MEAN
VALUE THEOREMS 349 A.3.2 PARTIAL DERIVATIVES 350 A.4 DIFFERENTIAL
EQUATIONS 351 A.4.1 EQUATIONS 351 A.4.2 WHAT IS A DIFFERENTIAL EQUATION?
351 A.4.3 STANDARD NOTATION 352 B COMPUTING 355 B.I DIFFERENTIAL
EQUATIONS 355 B.I.I ANALYTIC SOLUTIONS 356 B.1.2 NUMERICAL SOLUTIONS 357
B.2 TRIANGLE DANCE 365 B.3 ABOUT THE ACCOMPANYING SOFTWARE 366
BIBLIOGRAPHY 369 INDEX 37I
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| author | Scheinerman, Edward R. |
| author_facet | Scheinerman, Edward R. |
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| author_sort | Scheinerman, Edward R. |
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| dewey-ones | 003 - Systems |
| dewey-raw | 003/.85 |
| dewey-search | 003/.85 |
| dewey-sort | 13 285 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
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| id | DE-604.BV011247630 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:09:00Z |
| institution | BVB |
| isbn | 0131850008 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007549616 |
| oclc_num | 32469498 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-91 DE-BY-TUM DE-634 |
| physical | XVII, 373 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Prentice-Hall |
| record_format | marc |
| spellingShingle | Scheinerman, Edward R. Invitation to dynamical systems Dynamique différentiable ram Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4013396-5 |
| title | Invitation to dynamical systems |
| title_auth | Invitation to dynamical systems |
| title_exact_search | Invitation to dynamical systems |
| title_full | Invitation to dynamical systems Edward R. Scheinerman |
| title_fullStr | Invitation to dynamical systems Edward R. Scheinerman |
| title_full_unstemmed | Invitation to dynamical systems Edward R. Scheinerman |
| title_short | Invitation to dynamical systems |
| title_sort | invitation to dynamical systems |
| topic | Dynamique différentiable ram Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamique différentiable Differentiable dynamical systems Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007549616&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT scheinermanedwardr invitationtodynamicalsystems |
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Teilbibliothek Stammgelände
| Signatur: |
0002 MAT 344f 97 A 209
Lageplan |
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| Exemplar 1 | Ausleihbar Am Standort |