Recurrences and discrete dynamic systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin, [u.a.]
Springer
1980
|
| Schriftenreihe: | Lecture notes in mathematics
809 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 272 Seiten |
| ISBN: | 3540100172 0387100172 |
Internformat
MARC
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| 100 | 1 | |a Gumowski, Igor |d 1928-2019 |0 (DE-588)1077783469 |4 aut | |
| 245 | 1 | 0 | |a Recurrences and discrete dynamic systems |c Igor Gumowski ; Christian Mira |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c 1980 | |
| 300 | |a VI, 272 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 809 | |
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| 650 | 4 | |a Point mappings (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1809991530156392448 |
|---|---|
| adam_text |
CONTENTS
P-
Introduction and statement of the problem 1
Chapter I - Some properties of first order recurrences
1.0 Introduction 23
1.1 Elementary properties of first order recurrences 29
1.2 Singularity structure of a quadratic recurrence 38
1.3 Relation to functional equations 46
1.4 Topological entropy and some statistical properties 57
Chapter II - Some properties of second order recurrences
2.0 Introduction 61
2.1 Elementary properties of linear recurrences 65
2.2 The effect of non linear perturbations 76
2.3 Influence domain of a stable point singularity 81
2.4 Approximate determination of an isolated closed invariant curve 91
2.5 Some relationships between recurrences, continuous iterates and
differential equations 96
Chapter III - Stochasticity in conservative recurrences
3.0 Introduction 104
3.1 Quadratic recurrence 106
3.1.1. General properties 106
3.1.2. Ordering of cycles 111
3.1.3. Properties of invariant curves 116
3.1.4. Critical and exceptional cases 122
3.1.5. Bifurcations 129
3.2 Cubic recurrence !37
3.3 Bounded quadratic recurrence 148
3.4 Exponential recurrence 159
3.5 Sinusoidal recurrence 169
3.6 Unsymmetric sinusoidal recurrence 173
3.7 Box-within-a-box structure in the phase plane 177
3.8 The method of sections 179
3.9 Non-vanishing Jacobian and uniqueness of antecedents 181
3.10 The variational entropy 182
VI
Chapter IV - Stochasticity in almost conservative recurrences
4.0 Introduction 184
4.1 Quadratic recurrence 107
4.2 Effect of non-unique antecedents 201
Chapter V - Stochasticity in strongly non-conservative recurrences
5.0 Introduction 212
5.1 Effect of strong damping on an initially conservative recurrence 212
5.2 An elementary composite attractor 216
5.3 Chaos in a predator-prey recurrence 223
5.4 Chaos in a non-conservative recurrence with unique antecedents 229
Chapter VI - Conclusion and some open problems 234
References. 260
Index. 267 |
| any_adam_object | 1 |
| author | Gumowski, Igor 1928-2019 Mira, Christian 1934- |
| author_GND | (DE-588)1077783469 (DE-588)1121150233 |
| author_facet | Gumowski, Igor 1928-2019 Mira, Christian 1934- |
| author_role | aut aut |
| author_sort | Gumowski, Igor 1928-2019 |
| author_variant | i g ig c m cm |
| building | Verbundindex |
| bvnumber | BV002298410 |
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| dewey-full | 514/.72 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology 510 - Mathematics |
| dewey-raw | 514/.72 510 |
| dewey-search | 514/.72 510 |
| dewey-sort | 3514 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002298410 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-12T12:00:34Z |
| institution | BVB |
| isbn | 3540100172 0387100172 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001510647 |
| oclc_num | 6555328 |
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| physical | VI, 272 Seiten |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Gumowski, Igor 1928-2019 (DE-588)1077783469 aut Recurrences and discrete dynamic systems Igor Gumowski ; Christian Mira Berlin, [u.a.] Springer 1980 VI, 272 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 809 Applications ponctuelles (Mathématiques) Differentiaalsystemen gtt Dynamique différentielle Dynamische systemen gtt Modelos matemáticos Differentiable dynamical systems Point mappings (Mathematics) Rekursion (DE-588)4191814-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Rekurrenz (DE-588)7585550-1 gnd rswk-swf Diskretes System (DE-588)4401225-1 gnd rswk-swf Diskretes System (DE-588)4401225-1 s Dynamisches System (DE-588)4013396-5 s DE-604 Rekursion (DE-588)4191814-9 s Rekurrenz (DE-588)7585550-1 s Mira, Christian 1934- (DE-588)1121150233 aut Erscheint auch als Online-Ausgabe 978-3-540-38155-6 Lecture notes in mathematics 809 (DE-604)BV000676446 809 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001510647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gumowski, Igor 1928-2019 Mira, Christian 1934- Recurrences and discrete dynamic systems Lecture notes in mathematics Applications ponctuelles (Mathématiques) Differentiaalsystemen gtt Dynamique différentielle Dynamische systemen gtt Modelos matemáticos Differentiable dynamical systems Point mappings (Mathematics) Rekursion (DE-588)4191814-9 gnd Dynamisches System (DE-588)4013396-5 gnd Rekurrenz (DE-588)7585550-1 gnd Diskretes System (DE-588)4401225-1 gnd |
| subject_GND | (DE-588)4191814-9 (DE-588)4013396-5 (DE-588)7585550-1 (DE-588)4401225-1 |
| title | Recurrences and discrete dynamic systems |
| title_auth | Recurrences and discrete dynamic systems |
| title_exact_search | Recurrences and discrete dynamic systems |
| title_full | Recurrences and discrete dynamic systems Igor Gumowski ; Christian Mira |
| title_fullStr | Recurrences and discrete dynamic systems Igor Gumowski ; Christian Mira |
| title_full_unstemmed | Recurrences and discrete dynamic systems Igor Gumowski ; Christian Mira |
| title_short | Recurrences and discrete dynamic systems |
| title_sort | recurrences and discrete dynamic systems |
| topic | Applications ponctuelles (Mathématiques) Differentiaalsystemen gtt Dynamique différentielle Dynamische systemen gtt Modelos matemáticos Differentiable dynamical systems Point mappings (Mathematics) Rekursion (DE-588)4191814-9 gnd Dynamisches System (DE-588)4013396-5 gnd Rekurrenz (DE-588)7585550-1 gnd Diskretes System (DE-588)4401225-1 gnd |
| topic_facet | Applications ponctuelles (Mathématiques) Differentiaalsystemen Dynamique différentielle Dynamische systemen Modelos matemáticos Differentiable dynamical systems Point mappings (Mathematics) Rekursion Dynamisches System Rekurrenz Diskretes System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001510647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT gumowskiigor recurrencesanddiscretedynamicsystems AT mirachristian recurrencesanddiscretedynamicsystems |