Normal forms and unfoldings for local dynamical systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2003
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 481 - 487 |
| Beschreibung: | XIX, 494 S. graph. Darst. : 25 cm |
| ISBN: | 0387954643 |
Internformat
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| 500 | |a Literaturverz. S. 481 - 487 | ||
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Datensatz im Suchindex
| _version_ | 1804129839752413184 |
|---|---|
| adam_text | JAMES MURDOCK NORMAL FORMS AND UNFOLDINGS FOR LOCAL DYNAMICAL SYSTEMS
WITH 15 ILLUSTRATIONS SPRINGER CONTENTS PREFACE V 1 TWO EXAMPLES 1 1.1
THE (SINGLE) NONLINEAR CENTER 1 1.2 THE NONSEMISIMPLE DOUBLE-ZERO
EIGENVALUE 21 2 THE SPLITTING PROBLEM FOR LINEAR OPERATORS 27 2.1 THE
SPLITTING PROBLEM IN THE SEMISIMPLE CASE 28 2.2 SPLITTING BY MEANS OF AN
INNER PRODUCT 32 2.3 NILPOTENT OPERATORS 34 2.4 CANONICAL FORMS 39 2.5 *
AN INTRODUCTION TO SL(2) REPRESENTATION THEORY . . . . 47 2.6 *
ALGORITHMS FOR THE SL(2) SPLITTINGS 57 2.7 * OBTAINING SL(2) TRIADS 63 3
LINEAR NORMAL FORMS 69 3.1 PERTURBATIONS OF MATRICES 69 3.2 AN
INTRODUCTION TO THE FIVE FORMATS 74 3.3 NORMAL AND HYPERNORMAL FORMS
WHEN A O IS SEMISIMPLE 87 3.4 INNER PRODUCT AND SIMPLIFIED NORMAL FORMS
99 3.5 * THE SL(2) NORMAL FORM 118 3.6 LIE THEORY AND THE GENERATED
FORMATS 129 3.7 METANORMAL FORMS AND FC-DETERMINED HYPERBOLICITY . . .
142 XVIII CONTENTS 4 NONLINEAR NORMAL FORMS 157 4.1 PRELIMINARIES 157
4.2 SETTINGS FOR NONLINEAR NORMAL FORMS 160 4.3 THE DIRECT FORMATS (LA
AND LB) 164 4.4 LIE THEORY AND THE GENERATED FORMATS 174 4.5 THE
SEMISIMPLE NORMAL FORM 190 4.6 THE INNER PRODUCT AND SIMPLIFIED NORMAL
FORMS . . . . 221 4.7 THE MODULE STRUCTURE OF INNER PRODUCT AND
SIMPLIFIED NORMAL FORMS 242 4.8 * THE SL(2) NORMAL FORM 265 4.9 THE
HAMILTONIAN CASE 271 4.10 HYPERNORMAL FORMS FOR VECTOR FIELDS 283 5
GEOMETRICAL STRUCTURES IN NORMAL FORMS 295 5.1 PRESERVED STRUCTURES IN
TRUNCATED NORMAL FORMS . . . . 297 5.2 GEOMETRICAL STRUCTURES IN THE
FULL SYSTEM 316 5.3 ERROR ESTIMATES 323 5.4 THE NILPOTENT CENTER
MANIFOLD CASE 335 6 SELECTED TOPICS IN LOCAL BIFURCATION THEORY 339 6.1
BIFURCATIONS FROM A SINGLE-ZERO EIGENVALUE: A NEOCLASSICAL APPROACH
341 6.2 BIFURCATIONS FROM A SINGLE-ZERO EIGENVALUE: A MODERN APPROACH
356 6.3 UNFOLDING THE SINGLE-ZERO EIGENVALUE 366 6.4 UNFOLDING IN THE
PRESENCE OF GENERIC QUADRATIC TERMS 371 6.5 BIFURCATIONS FROM A SINGLE
CENTER (HOPF AND DEGENERATE HOPF BIFURCATIONS) 382 6.6 BIFURCATIONS FROM
THE NONSEMISIMPLE DOUBLE-ZERO EIGENVALUE (TAKENS-BOGDANOV BIFURCATIONS)
389 6.7 UNFOLDINGS OF MODE INTERACTIONS 396 A RINGS 405 A.I RINGS,
IDEALS, AND DIVISION 405 A.2 MONOMIALS AND MONOMIAL IDEALS 412 A.3 FLAT
FUNCTIONS AND FORMAL POWER SERIES 421 A.4 ORDERINGS OF MONOMIALS 424 A.5
DIVISION IN POLYNOMIAL RINGS; GROBNER BASES 427 A.6 DIVISION IN POWER
SERIES RINGS; STANDARD BASES 438 A.7 DIVISION IN THE RING OF GERMS 444 B
MODULES 447 B.I SUBMODULES OF 1 N 447 B.2 MODULES OF VECTOR FIELDS 449
CONTENTS XIX C FORMAT 2B: GENERATED RECURSIVE (HORI) 451 C.I FORMAT 2B,
LINEAR CASE (FOR CHAPTER 3) 451 C.2 FORMAT 2B, NONLINEAR CASE (FOR
CHAPTER 4) 457 D FORMAT 2C: GENERATED RECURSIVE (DEPRIT) 463 D.I FORMAT
2C, LINEAR CASE (FOR CHAPTER 3) 463 D.2 FORMAT 2C, NONLINEAR CASE (FOR
CHAPTER 4) 471 E ON SOME ALGORITHMS IN LINEAR ALGEBRA 477 REFERENCES 481
INDEX 489
|
| any_adam_object | 1 |
| author | Murdock, James A. |
| author_GND | (DE-588)172268427 |
| author_facet | Murdock, James A. |
| author_role | aut |
| author_sort | Murdock, James A. |
| author_variant | j a m ja jam |
| building | Verbundindex |
| bvnumber | BV016524638 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.8 |
| callnumber-search | QA614.8 |
| callnumber-sort | QA 3614.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 SK 810 |
| ctrlnum | (OCoLC)50749130 (DE-599)BVBBV016524638 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV016524638 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:11:31Z |
| institution | BVB |
| isbn | 0387954643 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010211857 |
| oclc_num | 50749130 |
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| owner | DE-20 DE-384 DE-11 DE-188 |
| owner_facet | DE-20 DE-384 DE-11 DE-188 |
| physical | XIX, 494 S. graph. Darst. : 25 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| spelling | Murdock, James A. Verfasser (DE-588)172268427 aut Normal forms and unfoldings for local dynamical systems James Murdock New York [u.a.] Springer 2003 XIX, 494 S. graph. Darst. : 25 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 481 - 487 Dynamique différentiable Formes normales (Mathématiques) Teoria da bifurcação (sistemas dinâmicos) larpcal Teoria das singularidades larpcal Differentiable dynamical systems Normal forms (Mathematics) Entfaltung Mathematik (DE-588)4014854-3 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Normalform (DE-588)4172025-8 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Normalform (DE-588)4172025-8 s Entfaltung Mathematik (DE-588)4014854-3 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211857&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Murdock, James A. Normal forms and unfoldings for local dynamical systems Dynamique différentiable Formes normales (Mathématiques) Teoria da bifurcação (sistemas dinâmicos) larpcal Teoria das singularidades larpcal Differentiable dynamical systems Normal forms (Mathematics) Entfaltung Mathematik (DE-588)4014854-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Normalform (DE-588)4172025-8 gnd |
| subject_GND | (DE-588)4014854-3 (DE-588)4137931-7 (DE-588)4172025-8 |
| title | Normal forms and unfoldings for local dynamical systems |
| title_auth | Normal forms and unfoldings for local dynamical systems |
| title_exact_search | Normal forms and unfoldings for local dynamical systems |
| title_full | Normal forms and unfoldings for local dynamical systems James Murdock |
| title_fullStr | Normal forms and unfoldings for local dynamical systems James Murdock |
| title_full_unstemmed | Normal forms and unfoldings for local dynamical systems James Murdock |
| title_short | Normal forms and unfoldings for local dynamical systems |
| title_sort | normal forms and unfoldings for local dynamical systems |
| topic | Dynamique différentiable Formes normales (Mathématiques) Teoria da bifurcação (sistemas dinâmicos) larpcal Teoria das singularidades larpcal Differentiable dynamical systems Normal forms (Mathematics) Entfaltung Mathematik (DE-588)4014854-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Normalform (DE-588)4172025-8 gnd |
| topic_facet | Dynamique différentiable Formes normales (Mathématiques) Teoria da bifurcação (sistemas dinâmicos) Teoria das singularidades Differentiable dynamical systems Normal forms (Mathematics) Entfaltung Mathematik Differenzierbares dynamisches System Normalform |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211857&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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