Flow lines and algebraic invariants in contact form geometry:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2003
|
| Series: | Progress in nonlinear differential equations and their applications
53 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | VII, 219 S. graph. Darst. |
| ISBN: | 0817643184 3764343184 |
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MARC
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| 100 | 1 | |a Bahri, Abbas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Flow lines and algebraic invariants in contact form geometry |c Abbas Bahri |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2003 | |
| 300 | |a VII, 219 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 53 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Global differential geometry | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Riemannian manifolds | |
| 830 | 0 | |a Progress in nonlinear differential equations and their applications |v 53 |w (DE-604)BV007934389 |9 53 | |
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Record in the Search Index
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|---|---|
| adam_text | ABBAS BAHRI FLOW LINES AND ALGEBRAIC INVARIANTS IN CONTACT FORM GEOMETRY
BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PROLOGUE 1 INTRODUCTION,
STATEMENT OF RESULTS, AND DISCUSSION OF RELATED HYPOTHESES 3 1
TOPOLOGICAL RESULTS 4 2 INTERMEDIATE HYPOTHESES (A4), (A4) , (A5), (A6)
7 3 THE NON-FREDHOLM CHARACTER OF THIS VARIATIONAL PROBLEM, THE
ASSOCIATED CONES, CONDITION (A5) (DISCUSSION AND REMOVAL).... 8 4.A
HYPOTHESIS (A4) AND STATEMENT OF THE MOST GENERAL RESULTS, DISCUSSION OF
(A4) 10 4.B DISCUSSION OF (A2), (A3), AND (A4) 12 OUTLINE OF THE BOOK 15
I REVIEW OF THE PREVIOUS RESULTS, SOME OPEN QUESTIONS.. 17 LA SETUP OF
THE VARIATIONAL PROBLEM 19 I.A.1 INTRODUCTION .-. 19 I.A.2 THE
VARIATIONAL FRAMEWORK 20 I.A.3 THE TOPOLOGY OF C P 22 I.A.4 BUNDLES AT
INFINITY , 26 I.AAA 7T2* AND THE SPACE OF V-VERTICALS, THE
CHARACTERISTIC PIECES 26 I.A.4.B THE ^-BUNDLES 26 I.A.4.C NEIGHBORHOODS
OF INFINITY 27 I.A.5 NON-FREDHOLM BEHAVIOR, ISOTOPIC DEFORMATION OF
CURVES .28 I.A.6 DESCRIPTION OF THE VARIOUS CRITICAL POINTS AT INFINITY
AND THEIR ASSOCIATED CONES 30 I.A.6.1 DESCRIPTION OF THE VARIOUS
CRITICAL POINTS AT INFINITY 30 I.A.6.2 THE DIFFERENCE OF TOPOLOGY 32
I.A.6.2.A THE MORSE INDEX, DIFFERENCE OF TOPOLOGY DUE TO A CRITICAL
POINT AT INFINITY OF THE FIRST TYPE AND NOT OF THE THIRD TYPE 32 I
CONTENTS I.A.6.2.B DIFFERENCE OF TOPOLOGY DUE TO A CRITICAL POINT OR
CRITICAL POINT AT INFINITY OF THE THIRD KIND 32 I.A.6.2.C DIFFERENCE OF
TOPOLOGY DUE TO A FALSE CRITICAL POINT AT INFINITY OF THE SECOND KIND Z~
34 I.A.6.2.D THE DIFFERENCE OF TOPOLOGY DUE TO A CRITICAL POINT AT
INFINITY OF THE SECOND AND THIRD KINDS 35 I.A.6.2.E THE DIFFERENCE OF
TOPOLOGY DUE TO A CRITICAL POINT AT INFINITY OF MIXED TYPE AND THE THIRD
KIND... 35 I.B THE FLOW Z O OF [2]: CRITICAL POINTS AT INFINITY, FALSE
AND TRUE 37 I.B.I A BRIEF DESCRIPTION OF THE FLOW ZO DEFINED IN [2] 37
I.B.2 THE //J-FLOW 39 I.B.3 THE FLOW AT INFINITY 49 I.B .4 FALSE
CRITICAL POINTS AT INFINITY OF THE FIRST TYPE 50 I.B .5 A JUSTIFICATION
OF THE FLOW DEFINED BY THE NORMALS 51 I.B.6 TRANSVERSALITY HOLDS 53 I.B
.7 A SKETCH OF THE DEFORMATION ARGUMENT OF [2] 55 I.B.8 SOME PRECISION
ABOUT THE SMALL NORMALS FLOW OF [2] 61 I.B .9 APPENDIX: THE EXIT SET
FROM INFINITY INTO CP 65 II INTERMEDIATE SECTION: RECALLING THE RESULTS
DESCRIBED IN THE INTRODUCTION, OUTLINING THE CONTENT OF THE NEXT
SECTIONS AND HOW THESE RESULTS ARE DERIVED 71 III TECHNICAL STUDY OF THE
CRITICAL POINTS AT INFINITY: VARIATIONAL THEORY WITHOUT THE FREDHOLM
HYPOTHESIS .. 75 III.A TRUE CRITICAL POINTS AT INFINITY 77 III.A.A ON
THE NUMBER OF ZEROS OF THE U-COMPONENT OF X ALONG 77 III.A.B THE
POINCARE -RETURN MAP OF A TRUE CRITICAL POINT AT INFINITY XQQ 78 III.A.C
THE MODIFICATION OF THE NUMBER OF ZEROS ON W U ( VQO): TRANSMUTATIONS 81
III.B FALSE CRITICAL POINTS AT INFINITY OF THE SECOND KIND 103 III.B.L A
HIDDEN COMPANION TO DEGENERATING PERIODIC ORBITS 103 III.B.2 CRITICAL
POINTS OF ?=I A, ON T^ 107 III.B.3 NORMALS IN C T AND LOCAL
PARAMETRIZATION NEAR A FALSE CRITICAL POINT AT INFINITY OF THE SECOND
KIND 109 III.B.3.A THE NORMALS IN C^ WHICH DO NOT INCREASE THE NUMBER OF
ZEROS OF B, AND THE RELATED CONDITIONS 109 CONTENTS VII III.B.3.B LOCAL
PARAMETRIZATION NEAR A FALSE INFINITY OF THE SECOND KIND 112 III.B.4 THE
NUMBER OF ZEROS ON THE UNSTABLE MANIFOLDS OF A FALSE CRITICAL POINT AT
INFINITY OF THE SECOND KIND. THE SELF-ADJUSTING DIRECTIONS OF THE NORMAL
INDEX 119 III.B.5 CHANGE OF PART OF THE NORMAL INDEX INTO THE TANGENTIAL
INDEX, OR VICE VERSA, AT A FALSE CRITICAL POINT AT INFINITY OF THE
SECOND KIND 123 III.B.6 CONES ASSOCIATED TO A FALSE CRITICAL POINT AT
INFINITY OF THE SECOND KIND 126 III.B.7 SINGULARITIES, CANCELLATIONS,
TRANSMUTATIONS ALONG DIFFERENTIABLE HOMOTOPIES 127 III.B.8 MORE 130
IILB.8.A MORE ON SINGULARITIES 130 III.B.8.B MORE ON TRANSMUTATIONS 133
III.B .9 THE POINCARE -RETURN MAP OF A FALSE CRITICAL POINT AT INFINITY
OF MIXED TYPE PRESERVES AREA 134 III.B.10 TOPOLOGICAL REMARKS 136 IV
REMOVAL OF (A5) 143 IV.L THE DIFFERENCE OF TOPOLOGY DUE TO A FALSE
CRITICAL POINT AT INFINITY OF THE THIRD KIND 145 IV.2 COMPLETION OF THE
REMOVAL OF (A5) 151 IV.3 CRITICAL POINTS AT INFINITY OF MIXED TYPE 191
IV.4 (A5) AND THE CRITICAL POINTS AT INFINITY OF THE THIRD KIND OR-OF
MIXED TYPE 193 V CONDITIONS (A2)-(A3)-(A4)-(A6) 195 V.I AN OUTLINE FOR
THE REMOVAL OF (A2) 197 V.2 DISCUSSION OF (A3) 207 V.3 WEAKENING
CONDITION (A4) 213 V.4 REMOVING CONDITION (A6) 215 REFERENCES 217
|
| any_adam_object | 1 |
| author | Bahri, Abbas |
| author_facet | Bahri, Abbas |
| author_role | aut |
| author_sort | Bahri, Abbas |
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| building | Verbundindex |
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| classification_tum | MAT 537f |
| ctrlnum | (OCoLC)50958866 (DE-599)BVBBV019364793 |
| dewey-full | 516.3/62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 |
| dewey-search | 516.3/62 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019364793 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:58:35Z |
| institution | BVB |
| isbn | 0817643184 3764343184 |
| language | English |
| lccn | 2002038316 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012828443 |
| oclc_num | 50958866 |
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| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | VII, 219 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Bahri, Abbas Verfasser aut Flow lines and algebraic invariants in contact form geometry Abbas Bahri Boston [u.a.] Birkhäuser 2003 VII, 219 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 53 Includes bibliographical references and index Global differential geometry Manifolds (Mathematics) Riemannian manifolds Progress in nonlinear differential equations and their applications 53 (DE-604)BV007934389 53 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012828443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bahri, Abbas Flow lines and algebraic invariants in contact form geometry Progress in nonlinear differential equations and their applications Global differential geometry Manifolds (Mathematics) Riemannian manifolds |
| title | Flow lines and algebraic invariants in contact form geometry |
| title_auth | Flow lines and algebraic invariants in contact form geometry |
| title_exact_search | Flow lines and algebraic invariants in contact form geometry |
| title_full | Flow lines and algebraic invariants in contact form geometry Abbas Bahri |
| title_fullStr | Flow lines and algebraic invariants in contact form geometry Abbas Bahri |
| title_full_unstemmed | Flow lines and algebraic invariants in contact form geometry Abbas Bahri |
| title_short | Flow lines and algebraic invariants in contact form geometry |
| title_sort | flow lines and algebraic invariants in contact form geometry |
| topic | Global differential geometry Manifolds (Mathematics) Riemannian manifolds |
| topic_facet | Global differential geometry Manifolds (Mathematics) Riemannian manifolds |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012828443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
| work_keys_str_mv | AT bahriabbas flowlinesandalgebraicinvariantsincontactformgeometry |