Morse theory for Hamiltonian systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2001
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| Series: | Chapman & Hall CRC research notes in mathematics series
425 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 189 S. graph. Darst. |
| ISBN: | 1584882026 |
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| 245 | 1 | 0 | |a Morse theory for Hamiltonian systems |c Alberto Abbondandolo |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2001 | |
| 300 | |a XI, 189 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Morse theorie |2 gtt | |
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| 650 | 7 | |a Sistemas hamiltonianos |2 larpcal | |
| 650 | 4 | |a Systèmes hamiltoniens | |
| 650 | 7 | |a Teoria de morse (geometria diferencial) |2 larpcal | |
| 650 | 4 | |a Hamiltonian systems | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
1 The Maslov index 1
1.1 The symplectic group 1
1.2 The Maslov index in dimension 2 4
1.2.1 The topology of Sp(2) 4
1.2.2 The rotation function on Sp(2) 5
1.2.3 The Maslov index for non degenerate paths in Sp(2) 9
1.3 The Maslov index in dimension 2N 10
1.3.1 The Krein signature on Sp{2N) 10
1.3.2 Normal forms of semi simple symplectic matrices . . 14
1.3.3 The topology of Sp(2Ar) 17
1.3.4 The rotation function on Sp(2N) 19
1.3.5 Decomposition of Sp{2N) 24
1.3.6 The Maslov index of non degenerate paths in Sp{2N) 28
1.3.7 The Maslov index of degenerate paths in Sp(2N) . . 31
1.4 The Maslov index of a linear Hamiltonian system 32
1.4.1 Iteration formulas 33
1.5 The Maslov index of an autonomous system 37
1.6 Some bibliography and further remarks 41
2 The relative Morse index 43
2.1 Commensurable spaces and relative dimension 43
2.1.1 Further properties 46
2.2 Fredholm pairs of subspaces 49
2.3 Relative Morse index of quadratic forms 51
2.3.1 Further properties 55
2.4 Relative Morse index of critical points 57
2.5 Finite dimensional reductions 58
2.6 Some bibliography and further remarks 62
v
vj Contents
3 Functional setting 63
3.1 Fractional Sobolev spaces 63
3.2 Linear Hamiltonian systems 67
3.2.1 Comparison between the relative Morse index and the
Maslov index 69
3.3 Nonlinear Hamiltonian systems 74
3.4 Linear Lagrangian systems 78
3.4.1 Comparison between the Morse index and the Maslov
index 80
3.5 Nonlinear Lagrangian systems 83
3.6 Some bibliography and further remarks 85
4 Superquadratic Hamiltonians 87
4.1 Abstract critical point theory 87
4.1.1 The (PS) and (PS)* condition 87
4.1.2 A review of Morse theory 90
4.1.3 Linking theorems and Morse index estimates .... 94
4.1.4 Strongly indefinite functionals 97
4.2 Superquadratic Hamiltonians 100
4.2.1 Minimality of the period 108
4.3 A Birkhoff Lewis type theorem 110
4.4 Some bibliography and further remarks 117
5 Asymptotically linear systems 119
5.1 Non resonant systems 120
5.1.1 Abstract asymptotically quadratic functionals .... 120
5.1.2 Morse relations for non resonant systems 126
5.1.3 Solutions of higher period 129
5.2 Morse relations for autonomous systems 131
5.2.1 Growth of the number of periodic solutions of
autonomous systems 132
5.3 Systems with resonance at infinity 136
5.3.1 Abstract asymptotically quadratic functionals,
degenerate at infinity 136
5.3.2 Resonant systems 147
5.4 Some bibliography and further remarks 151
6 The Arnold conjectures for symplectic fixed points 153
6.1 The Arnold conjectures 153
6.1.1 Hamiltonian diffeomorphisms of the two torus . ... 156
6.1.2 Non degenerate fixed points on the torus 160
6.1.3 Degenerate fixed points on the torus 163
6.2 The Arnold conjectures on the projective space 165
Contents vii
6.3 Periodic points on the torus 169
6.4 Some bibliography and further remarks 171
Bibliography 173
Index 187
|
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| id | DE-604.BV013828926 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:52:45Z |
| institution | BVB |
| isbn | 1584882026 |
| language | English |
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| owner_facet | DE-824 DE-11 |
| physical | XI, 189 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Chapman & Hall CRC research notes in mathematics series |
| series2 | Chapman & Hall CRC research notes in mathematics series |
| spelling | Abbondandolo, Alberto Verfasser aut Morse theory for Hamiltonian systems Alberto Abbondandolo Boca Raton [u.a.] Chapman & Hall/CRC 2001 XI, 189 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC research notes in mathematics series 425 Hamiltonianen gtt Morse theorie gtt Morse, Théorie de Sistemas dinâmicos larpcal Sistemas hamiltonianos larpcal Systèmes hamiltoniens Teoria de morse (geometria diferencial) larpcal Hamiltonian systems Morse theory Morse-Theorie (DE-588)4197103-6 gnd rswk-swf Morse-Theorie (DE-588)4197103-6 s DE-604 Chapman & Hall CRC research notes in mathematics series 425 (DE-604)BV012456897 425 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009457761&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abbondandolo, Alberto Morse theory for Hamiltonian systems Chapman & Hall CRC research notes in mathematics series Hamiltonianen gtt Morse theorie gtt Morse, Théorie de Sistemas dinâmicos larpcal Sistemas hamiltonianos larpcal Systèmes hamiltoniens Teoria de morse (geometria diferencial) larpcal Hamiltonian systems Morse theory Morse-Theorie (DE-588)4197103-6 gnd |
| subject_GND | (DE-588)4197103-6 |
| title | Morse theory for Hamiltonian systems |
| title_auth | Morse theory for Hamiltonian systems |
| title_exact_search | Morse theory for Hamiltonian systems |
| title_full | Morse theory for Hamiltonian systems Alberto Abbondandolo |
| title_fullStr | Morse theory for Hamiltonian systems Alberto Abbondandolo |
| title_full_unstemmed | Morse theory for Hamiltonian systems Alberto Abbondandolo |
| title_short | Morse theory for Hamiltonian systems |
| title_sort | morse theory for hamiltonian systems |
| topic | Hamiltonianen gtt Morse theorie gtt Morse, Théorie de Sistemas dinâmicos larpcal Sistemas hamiltonianos larpcal Systèmes hamiltoniens Teoria de morse (geometria diferencial) larpcal Hamiltonian systems Morse theory Morse-Theorie (DE-588)4197103-6 gnd |
| topic_facet | Hamiltonianen Morse theorie Morse, Théorie de Sistemas dinâmicos Sistemas hamiltonianos Systèmes hamiltoniens Teoria de morse (geometria diferencial) Hamiltonian systems Morse theory Morse-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009457761&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012456897 |
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