Discrete dynamical systems and difference equations with Mathematica:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2002
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 327-339) and index |
| Physical Description: | XV, 344 S. graf. Darst. |
| ISBN: | 1584882875 |
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Record in the Search Index
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| adam_text | DISCRETE DYNAMICAL SYSTEMS AND DIFFERENCE EQUATIONS WITH MATHEMATICS
MUSTAFA R.S. KULENOVIC ORLANDO MERINO DEPARTMENT OF MATHEMATICS
UNIVERSITY OF RHODE ISLAND KINGSTON, RHODE ISLAND CHAPMAN & HALL/CRC A
CRG-PRESS-GOMPANY BOCA RATON LONDON NEW YORK * WASHINGTON, D.C. CONTENTS
DYNAMICS OF ONE-DIMENSIONAL DYNAMICAL SYSTEMS 1 1.1 INTRODUCTION 1 1.2
LINEAR DIFFERENCE EQUATIONS WITH CONSTANT COEFFICIENTS . . . . 2 1.3
LINEAR DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS 4 1.4 STABILITY 5
1.4.1 VISUALIZATION OF ORBITS AND TIME SERIES 8 1.5 STABILITY IN THE
NONHYPERBOLIC CASE 14 1.5.1 THE CASE / (*) = 1 .... . 14 1.5.2 THE CASE
/ (*) = -1 17 1.6 BIFURCATIONS 19 1.6.1 SHARKOVSKY S THEOREM AND PERIOD
DOUBLING 22 1.7 DYNAMICA SESSION 26 1.7.1 ORBITS AND PERIODIC POINTS 26
1.7.2 STABILITY AND MULTIPLIERS 34 1.7.3 BIFURCATION DIAGRAMS 39 1.7.4
LYAPUNOV NUMBERS 41 1.7.5 BOX DIMENSION 45 1.8 SYMBOLIC DYNAMICS FOR
ONE-DIMENSIONAL MAPS 47 1.8.1 THE CANTOR SET 47 1.8.2 SYMBOLIC DYNAMICS
AND CHAOS IN THE SENSE OF DEVANEY 49 1.8.3 DYNAMICA SESSION 55 1.9
DISSIPATIVE MAPS AND GLOBAL ATTRACTIVITY 61 1.10 PARAMETRIZATION AND THE
POINCARE FUNCTIONAL EQUATION . . . . 65 1.11 EXERCISES 67 DYNAMICS OF
TWO-DIMENSIONAL DYNAMICAL SYSTEMS 75 2.1 INTRODUCTION 75 2.2 LINEAR
THEORY 76 2.2.1 TWO-DIMENSIONAL LINEAR SYSTEMS 76 2.2.2 POWERS OF A
MATRIX AND JORDAN NORMAL FORM 78 2.2.3 SECOND ORDER LINEAR EQUATIONS 79
2.3 EQUILIBRIUM SOLUTIONS 84 2.3.1 EXAMPLES 85 2.4 THE RICCATI EQUATION
87 2.4.1 THE RICCATI NUMBER AND CHANGES OF VARIABLES 88 2.4.2 THE CASE
WHEN A+J3 = 0 89 VN VLLL 2.4.3 THE CASE WHEN A+J30 AND/? = 90 2.4.4
THE CASE WHEN A +/3 0 AND R 92 2.4.5 THE CASE WHEN A +/3 4- 0 AND
R 95 2.5 LINEARIZED STABILITY ANALYSIS 97 2.6 DYNAMICA SESSION 102
2.7 PERIOD-DOUBLING BIFURCATION 105 2.8 LYAPUNOV NUMBERS 106 2.9 BOX
DIMENSION 110 2.10 SEMICYCLE ANALYSIS 112 2.11 STABLE AND UNSTABLE
MANIFOLDS 117 2.12 DYNAMICA SESSION ON HENON S EQUATION 122 2.13
INVARIANTS 131 2.14 LYAPUNOV FUNCTIONS, STABILITY, AND INVARIANTS 134
2.15 DYNAMICA SESSION ON LYNESS MAP 137 2.16 DISSIPATIVE MAPS AND
SYSTEMS 149 2.17 DYNAMICA SESSION ON A RATIONAL DIFFERENCE EQUATION 152
2.17.1 STABILITY ANALYSIS OF THE EQUILIBRIUM 153 2.17.2 PRIME PERIOD-TWO
SOLUTIONS 156 2.17.3 NUMERICAL EXPLORATIONS 160 2.18 AREA-PRESERVING
MAPS AND SYSTEMS 165 2.19 BIOLOGY APPLICATIONS PROJECTS 172 2.20
APPLICATIONS IN ECONOMICS 188 2.21 EXERCISES 191 SYSTEMS OF DIFFERENCE
EQUATIONS, STABILITY, AND SEMICYCLES 201 3.1 INTRODUCTION 201 3.2
LINEAR THEORY 201 3.2.1 JORDAN NORMAL FORM 202 3.2.2 LINEAR
NONHOMOGENEOUS SYSTEM 204 3.2.3 LINEAR DIFFERENCE EQUATIONS OF K-TH.
ORDER 205 3.3 STABILITY OF LINEAR SYSTEMS 207 3.3.1 NORMS OF VECTORS AND
MATRICES 207 3.3.2 BASIC NOTIONS OF STABILITY 209 3.4 THE ROUTH-HURWITZ
AND SCHUR-COHN CRITERIA 211 3.5 NONLINEAR SYSTEMS AND STABILITY 214
3.5.1 LINEARIZED STABILITY 215 3.5.2 LYAPUNOV FUNCTIONS AND STABILITY
216 3.6 LIMIT SETS AND INVARIANT MANIFOLDS 218 3.7 DISSIPATIVE MAPS 226
3.8 STABILITY OF DIFFERENCE EQUATIONS 227 3.9 SEMICYCLE ANALYSIS ^ 229
3.10 DYNAMICA SESSIO N ON SEMICYCLES 229 3.10.1 LYNESS EQUATION 229
3.10.2 TODD S EQUATION 230 IX 3.10.3 GINGERBREADMAN EQUATION 232 3.10.4
RATIONAL EQUATION 235 3.10.5 CONCLUSION 237 3.11 EXERCISES 237
INVARIANTS AND RELATED LYAPUNOV FUNCTIONS 243 4.1 INTRODUCTION 243 4.2
INVARIANTS FOR LINEAR EQUATIONS AND SYSTEMS 245 4.3 INVARIANTS AND
CORRESPONDING LYAPUNOV FUNCTIONS FOR NONLIN- EAR SYSTEMS 246 4.3.1
APPLICATIONS 247 4.4 INVARIANTS OF A SPECIAL CLASS OF DIFFERENCE
EQUATIONS 252 4.4.1 APPLICATIONS 254 4.5 DYNAMICA SESSION ON INVARIANTS
259 4.5.1 INTRODUCTION 259 4.5.2 AN INVARIANT FOR LYNESS-TYPE EQUATION
260 4.5.3 SPECIFYING A BASIS FOR THE INVARIANT, PART I 261 4.5.4
SPECIFYING A BASIS FOR THE INVARIANT, PART II 262 4.6 DYNAMICA SESSION
ON LYAPUNOV FUNCTIONS 263 4.7 INVARIANCE UNDER LIE GROUP TRANSFORMATIONS
266 4.8 EXERCISES 268 DYNAMICS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS
273 5.1 INTRODUCTION 273 5.2 DYNAMICA SESSION ON THIRD ORDER DIFFERENCE
EQUATIONS .... 275 5.2.1 NUMERICAL EXPLORATIONS 276 5.3 DISSIPATIVE
DIFFERENCE EQUATION OF THIRD ORDER 279 5.3.1 INTRODUCTION 279 5.4
DYNAMICA SESSION ON LOCAL ASYMPTOTIC STABILITY OF PERIOD-TWO SOLUTIONS
282 5.4.1 INTRODUCTION 282 5.4.2 A QUADRATIC EQUATION SATISFIED BY
PERIOD-TWO SOLUTIONS 282 5.4.3 MAIN RESULTS 283 5.4.4 CONDITIONS FOR
LINEARIZED LOCAL STABILITY 284 5.4.5 FORMULAS FOR A AND B IN TERMS OF P,
Q 286 5.4.6 BOUNDS FOR A AND B 287 5.4.7 COMPLETION OF THE PROOF OF
STABILITY 288 5.5 DYNAMICA SESSION ON TODD S DIFFERENCE EQUATION 288
5.5.1 SUMMARY OF RESULTS AND OPEN PROBLEMS 299 5.6 BIOLOGY APPLICATIONS
PROJECTS 300 5.7 EXERCISES 302 6 FRACTALS GENERATED BY ITERATED FUNCTION
SYSTEMS 305 6.1 INTRODUCTION 305 6.2 BASIC DEFINITIONS AND RESULTS 307
6.3 ITERATED FUNCTION SYSTEMS 308 6.4 BASIC RESULTS ON ITERATED FUNCTION
SYSTEMS 314 6.5 CALCULATION OF BOX DIMENSION FOR IFS 316 6.6 DYNAMICA
SESSION 318 6.7 EXERCISES 325 BIBLIOGRAPHY 327 INDEX 341
|
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| spelling | Kulenović, Mustafa R. S. Verfasser aut Discrete dynamical systems and difference equations with Mathematica Mustafa R.S. Kulenović, Orlando Merino Boca Raton [u.a.] Chapman & Hall/CRC 2002 XV, 344 S. graf. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 327-339) and index Mathematica (Computer file) Mathematica (logiciel) ram Équations aux différences - Informatique Équations aux différences ram Datenverarbeitung Difference equations Data processing Dynamisches System (DE-588)4013396-5 gnd rswk-swf Diskretes System (DE-588)4401225-1 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Diskretes System (DE-588)4401225-1 s Dynamisches System (DE-588)4013396-5 s Differenzengleichung (DE-588)4012264-5 s Mathematica Programm (DE-588)4268208-3 s DE-604 Merino, Orlando Sonstige (DE-588)120340803X oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009841270&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kulenović, Mustafa R. S. Discrete dynamical systems and difference equations with Mathematica Mathematica (Computer file) Mathematica (logiciel) ram Équations aux différences - Informatique Équations aux différences ram Datenverarbeitung Difference equations Data processing Dynamisches System (DE-588)4013396-5 gnd Diskretes System (DE-588)4401225-1 gnd Differenzengleichung (DE-588)4012264-5 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4401225-1 (DE-588)4012264-5 (DE-588)4268208-3 |
| title | Discrete dynamical systems and difference equations with Mathematica |
| title_auth | Discrete dynamical systems and difference equations with Mathematica |
| title_exact_search | Discrete dynamical systems and difference equations with Mathematica |
| title_full | Discrete dynamical systems and difference equations with Mathematica Mustafa R.S. Kulenović, Orlando Merino |
| title_fullStr | Discrete dynamical systems and difference equations with Mathematica Mustafa R.S. Kulenović, Orlando Merino |
| title_full_unstemmed | Discrete dynamical systems and difference equations with Mathematica Mustafa R.S. Kulenović, Orlando Merino |
| title_short | Discrete dynamical systems and difference equations with Mathematica |
| title_sort | discrete dynamical systems and difference equations with mathematica |
| topic | Mathematica (Computer file) Mathematica (logiciel) ram Équations aux différences - Informatique Équations aux différences ram Datenverarbeitung Difference equations Data processing Dynamisches System (DE-588)4013396-5 gnd Diskretes System (DE-588)4401225-1 gnd Differenzengleichung (DE-588)4012264-5 gnd Mathematica Programm (DE-588)4268208-3 gnd |
| topic_facet | Mathematica (Computer file) Mathematica (logiciel) Équations aux différences - Informatique Équations aux différences Datenverarbeitung Difference equations Data processing Dynamisches System Diskretes System Differenzengleichung Mathematica Programm |
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