Difference equations and their applications:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht, [u.a.]
Kluwer Academic Publishers
[1993]
|
| Schriftenreihe: | Mathematics and its applications
250 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | xii, 358 Seiten |
| ISBN: | 0792321944 |
Internformat
MARC
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| 240 | 1 | 0 | |a Raznostnye uravnenija i ich priloženija |
| 245 | 1 | 0 | |a Difference equations and their applications |c by A. N. Sharkovsky ; Yu. L. Maistrenko and E. Yu. Romanenko |
| 264 | 1 | |a Dordrecht, [u.a.] |b Kluwer Academic Publishers |c [1993] | |
| 264 | 4 | |c © 1993 | |
| 300 | |a xii, 358 Seiten | ||
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| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1807503778349318144 |
|---|---|
| adam_text |
Contents
Notation ix
Preface xi
Introduction 1
Parti. ONE DIMENSIONAL DYNAMICAL SYSTEMS 15
1. Introduction to the Theory of Dynamical Systems 15
§1. Are One Dimensional Dynamical Systems Simple? 17
§2. What May Occur in One Dimensional Dynamical Systems.
Some Notions and Examples 23
§3. Intermixing (Strange) Attractors 37
2. Periodic Trajectories 45
§1. Attracting Fixed Points 45
§2. Coexistence of Cycles 52
§3 Bifurcations of Cycles 63
3. Behavior of Trajectories 71
§1. Trajectories of Simple Dynamical Systems 71
§2. Return of Points and Sets 75
§3. Criteria of Simplicity and Complexity for Maps 81
§4 Stability of Trajectories and Dynamical Systems 84
4. Dynamical Systems for b' Maps 95
§1. Unimodal Maps 95
§2. Schwarzian and Attracting Cycles 98
§3. Periodic Intervals 101
§4. Spectral Decomposition of the Set of Non Wandering Points 111
§5. Bifurcations of the Periodic Intervals and Stability
of the Spectral Decomposition 119
vi Contents
Part II. DIFFERENCE EQUATIONS WITH
CONTINUOUS TIME 125
1. Nonlinear Difference Equations 125
§ 1. S tatement of the Problem 125
§2. Asymptotically Discontinuous Solutions 134
§3. Separator of a Map. The Simplest Properties of
Asymptotically Discontinuous Solutions 139
§4. The Limiting Semi Group 143
§5. Asymptotic Behavior of Asymptotically
Discontinuous Solutions 152
§6. Stability of Asymptotically Discontinuous Solutions 155
2. Difference Equations with U Nonlinearity 159
§1. Limiting Semi Group, Separator, Spectrum of Jumps 159
§2. Spectrum of Asymptotic Jumps. Solutions of
Relaxation and Turbulent Types 163
§3. Stability and Bifurcations of Solutions 175
§4. Emergence of Ordered Structures 183
Part III. DIFFERENTIAL DIFFERENCE EQUATIONS 187
1. Completely Integrable Differential Difference Equations 188
§ 1. What Kind of Asymptotic Behavior of Solutions of
Differential Difference Equations One May Expect 188
§2. Equations with a Decomposable Operator. Completely
Integrable Differential Difference Equations 193
§3. Connection Between Solutions of Completely Integrable
Differential Difference Equations and Solutions of the
Corresponding Difference Equations. The Phase Plane Method 197
§4. Periodic Solutions of Completely Integrable Differential
Difference Equations. Their Exceptional Character 206
§5. Asymptotically Periodic Solutions of Completely Integrable
Equations. Their Typicalness 211
2. Differential Difference Equations Close To Difference Ones 223
§ 1. General Definitions and Properties 223
§2. Asymptotic Behavior of Solutions of the Perturbed Equation 227
§3. Stability of Solutions 234
Contents vii
3. Singularly Perturbed Differential Difference Equations 239
§ 1. Statement of the Problem. Continuous Dependence of
Solutions on the Parameter v on a Finite Interval 239
§2. Invariance of the Asymptotic Properties of Solutions 243
§3. Behavior of Solutions as t » °° 248
Part IV. BOUNDARY VALUE PROBLEMS FOR
HYPERBOLIC SYSTEMS OF PARTIAL
DIFFERENTIAL EQUATIONS 273
1. Reduction of Boundary Value Problems to Difference and
Differential Difference Equations 21A
§ 1. Reduction to a Nonlinear Difference Equation 274
§2. Reduction to Differential Difference Equations 277
§3. Reduction Procedure in More General Situations 279
2. Boundary Value Problem for a System with Small Parameter 285
§ 1. Boundary Value Problem for a Non Perturbed System 285
§2. The Case of e 0. Existence of Solution and Extendability 290
§3. Stability in the Hausdorff Metric 292
§4. Stability in the Skorokhod Metric and Asymptotic Periodicity 297
3. Boundary Value Problem for Systems with Two Spatial Variables 305
§ 1. Statement of the problem, Its Correctness. Reduction to a
Difference Equation 305
§2. Solution of the Boundary Value Problem in the Case of
Linear B oundary Conditions 310
§3. Nonlinear Boundary Conditions. Exclusion of the "Mean Row" 313
§4. Asymptotic Behavior of Solutions as t » °° 318
§5 Self Stochasticity 330
References 335
Index 357 |
| any_adam_object | 1 |
| author | Šarkovskij, Aleksandr N. 1936-2022 Maistrenko, Yuri Romanenko, Elena Ju |
| author_GND | (DE-588)172587069 (DE-588)1089338864 (DE-588)17258454X |
| author_facet | Šarkovskij, Aleksandr N. 1936-2022 Maistrenko, Yuri Romanenko, Elena Ju |
| author_role | aut aut aut |
| author_sort | Šarkovskij, Aleksandr N. 1936-2022 |
| author_variant | a n š an anš y m ym e j r ej ejr |
| building | Verbundindex |
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| classification_rvk | SK 580 SK 950 |
| classification_tum | MAT 390f PHY 013f |
| ctrlnum | (OCoLC)246726143 (DE-599)BVBBV007071454 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV007071454 |
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| indexdate | 2024-08-16T00:58:50Z |
| institution | BVB |
| isbn | 0792321944 |
| language | English |
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| physical | xii, 358 Seiten |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Academic Publishers |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Šarkovskij, Aleksandr N. 1936-2022 (DE-588)172587069 aut Raznostnye uravnenija i ich priloženija Difference equations and their applications by A. N. Sharkovsky ; Yu. L. Maistrenko and E. Yu. Romanenko Dordrecht, [u.a.] Kluwer Academic Publishers [1993] © 1993 xii, 358 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 250 Aus dem Russ. übers. Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Lösung Mathematik (DE-588)4120678-2 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 s Mathematische Physik (DE-588)4037952-8 s DE-604 Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 Anwendung (DE-588)4196864-5 s 2\p DE-604 Lösung Mathematik (DE-588)4120678-2 s 3\p DE-604 Maistrenko, Yuri (DE-588)1089338864 aut Romanenko, Elena Ju. (DE-588)17258454X aut Erscheint auch als Online-Ausgabe 978-94-011-1763-0 Mathematics and its applications 250 (DE-604)BV008163334 250 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004494103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Šarkovskij, Aleksandr N. 1936-2022 Maistrenko, Yuri Romanenko, Elena Ju Difference equations and their applications Mathematics and its applications Differenzengleichung (DE-588)4012264-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Mathematische Physik (DE-588)4037952-8 gnd Lösung Mathematik (DE-588)4120678-2 gnd Anwendung (DE-588)4196864-5 gnd |
| subject_GND | (DE-588)4012264-5 (DE-588)4012249-9 (DE-588)4037952-8 (DE-588)4120678-2 (DE-588)4196864-5 |
| title | Difference equations and their applications |
| title_alt | Raznostnye uravnenija i ich priloženija |
| title_auth | Difference equations and their applications |
| title_exact_search | Difference equations and their applications |
| title_full | Difference equations and their applications by A. N. Sharkovsky ; Yu. L. Maistrenko and E. Yu. Romanenko |
| title_fullStr | Difference equations and their applications by A. N. Sharkovsky ; Yu. L. Maistrenko and E. Yu. Romanenko |
| title_full_unstemmed | Difference equations and their applications by A. N. Sharkovsky ; Yu. L. Maistrenko and E. Yu. Romanenko |
| title_short | Difference equations and their applications |
| title_sort | difference equations and their applications |
| topic | Differenzengleichung (DE-588)4012264-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Mathematische Physik (DE-588)4037952-8 gnd Lösung Mathematik (DE-588)4120678-2 gnd Anwendung (DE-588)4196864-5 gnd |
| topic_facet | Differenzengleichung Differentialgleichung Mathematische Physik Lösung Mathematik Anwendung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004494103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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