Shortest paths for sub-Riemannian metrics on rank-two distributions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
1995
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| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
564 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 118, Number 564 (second of 5 numbers) 2. Verf. in der Vorlage faelschlicherweise als "Sussman, Héctor J." bezeichnet |
| Physical Description: | IX, 104 S. |
| ISBN: | 0821804049 |
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Record in the Search Index
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| adam_text | MEMOIRS -!-* A OF THE AMERICAN MATHEMATICAL SOCIETY NUMBER 564 SHORTEST
PATHS FOR SUB-RIEMANNIAN METRICS ON RANK-TWO DISTRIBUTIONS WENSHENG LIU
HECTOR J. SUSSMANN NOVEMBER 1995 * VOLUME 118 * NUMBER 564 (SECOND OF 5
NUMBERS) * ISSN 0065-9266 AMERICAN MATHEMATICAL SOCIETY- PROVIDENCE,
RHODE ISLAND TABLE OF CONTENTS 1 INTRODUCTION 1 2 THREE EXAMPLES 8 2.1
RIEMANNIAN GEODESIES 9 2.2 THE HEISENBERG ALGEBRA CASE 10 2.3 AN
ABNORMAL MINIMIZER 12 3 NOTATIONAL CONVENTIONS AND DEFINITIONS 16 3.1
MANIFOLDS, CHARTS, BUNDLES, CURVES AND ARCS 16 3.2 HAMILTONIAN
FUNCTIONS, HAMILTON VECTOR FIELDS, AND BICHARACTERISTICS 17 3.3
HAMILTONIAN LIFTS AND CHARACTERISTICS 18 3.4 DISTRIBUTIONS, ADMISSIBLE
CURVES, ORBITS 19 3.5 NONHOLONOMIC DISTRIBUTIONS; REGULARITY 20 4
ABNORMAL EXTREMALS 22 5 SUB-RIEMANNIAN MANIFOLDS, LENGTH MINIMIZERS AND
EXTREMALS 25 5.1 THE SUB-RIEMANNIAN DISTANCE, LENGTH MINIMIZATION AND
TIME OPTIMALITY 26 5.2 EXTREMALS 29 5.3 THE RELATIONSHIP BETWEEN
MINIMALITY AND EXTREMALITY 31 6 REGULAR ABNORMAL EXTREMALS FOR RANK-TWO
DISTRIBUTIONS 33 6.1 THE REGULAR ABNORMAL FOLIATION OF A RANK-TWO
DISTRIBUTION 33 6.2 REGULAR ABNORMAL BIEXTREMALS OF A SUB-RIEMANNIAN
MANIFOLD 41 7 LOCAL OPTIMALITY OF REGULAR ABNORMAL EXTREMALS 43 7.1 THE
MAIN INEQUALITY 46 VII VIII CONTENTS 7.2 THE NORMAL FORM THEOREM 51 7.3
THE OPTIMALITY THEOREM 59 8 STRICT ABNORMALITY 60 9 SOME SPECIAL CASES
61 9.1 2- AND 3-GENERATING DISTRIBUTIONS 62 9.2 3-REGULAR DISTRIBUTIONS
62 9.3 THE 4- AND 5-DIMENSIONAL CASES 68 9.4 THE THREE-DIMENSIONAL CASE
72 9.5 A LIE GROUP EXAMPLE 73 9.6 A NONSMOOTH ABNORMAL EXTREMAL 74
APPENDIX A: THE GAVEAU*BROCKETT PROBLEM 75 APPENDIX B: PROOF OF THEOREM
1 81 B.I: CONTROL SYSTEMS 81 B.2: THE MAXIMUM PRINCIPLE 84 APPENDIX C:
LOCAL OPTIMALITY OF NORMAL EXTREMALS 89 APPENDIX D: RIGID SUB-RIEMANNIAN
ARCS AND LOCAL OPTI- MALITY 92 APPENDIX E: A NONOPTIMALITY PROOF 99
REFERENCES 102
|
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| id | DE-604.BV010544974 |
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| indexdate | 2024-07-09T17:54:48Z |
| institution | BVB |
| isbn | 0821804049 |
| language | English |
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| physical | IX, 104 S. |
| publishDate | 1995 |
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| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Liu, Wensheng 1962- Verfasser (DE-588)17293110X aut Shortest paths for sub-Riemannian metrics on rank-two distributions Wensheng Liu ; Héctor J. Sussman Providence, RI 1995 IX, 104 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 564 Volume 118, Number 564 (second of 5 numbers) 2. Verf. in der Vorlage faelschlicherweise als "Sussman, Héctor J." bezeichnet Differentiaalmeetkunde gtt Geodeten gtt Riemann-vlakken gtt Geodesics (Mathematics) Geometry, Riemannian Riemannsche Metrik (DE-588)4294399-1 gnd rswk-swf Geodätische Linie (DE-588)4156669-5 gnd rswk-swf Geodätische Linie (DE-588)4156669-5 s Riemannsche Metrik (DE-588)4294399-1 s DE-604 Sussman, Héctor J. 1946- Verfasser (DE-588)172931118 aut American Mathematical Society: Memoirs of the American Mathematical Society 564 (DE-604)BV008000141 564 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007028179&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liu, Wensheng 1962- Sussman, Héctor J. 1946- Shortest paths for sub-Riemannian metrics on rank-two distributions American Mathematical Society: Memoirs of the American Mathematical Society Differentiaalmeetkunde gtt Geodeten gtt Riemann-vlakken gtt Geodesics (Mathematics) Geometry, Riemannian Riemannsche Metrik (DE-588)4294399-1 gnd Geodätische Linie (DE-588)4156669-5 gnd |
| subject_GND | (DE-588)4294399-1 (DE-588)4156669-5 |
| title | Shortest paths for sub-Riemannian metrics on rank-two distributions |
| title_auth | Shortest paths for sub-Riemannian metrics on rank-two distributions |
| title_exact_search | Shortest paths for sub-Riemannian metrics on rank-two distributions |
| title_full | Shortest paths for sub-Riemannian metrics on rank-two distributions Wensheng Liu ; Héctor J. Sussman |
| title_fullStr | Shortest paths for sub-Riemannian metrics on rank-two distributions Wensheng Liu ; Héctor J. Sussman |
| title_full_unstemmed | Shortest paths for sub-Riemannian metrics on rank-two distributions Wensheng Liu ; Héctor J. Sussman |
| title_short | Shortest paths for sub-Riemannian metrics on rank-two distributions |
| title_sort | shortest paths for sub riemannian metrics on rank two distributions |
| topic | Differentiaalmeetkunde gtt Geodeten gtt Riemann-vlakken gtt Geodesics (Mathematics) Geometry, Riemannian Riemannsche Metrik (DE-588)4294399-1 gnd Geodätische Linie (DE-588)4156669-5 gnd |
| topic_facet | Differentiaalmeetkunde Geodeten Riemann-vlakken Geodesics (Mathematics) Geometry, Riemannian Riemannsche Metrik Geodätische Linie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007028179&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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