Elements of the mathematical theory of multi-frequency oscillations:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer
1991
|
| Schriftenreihe: | Mathematics and its applications / Soviet series
71 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003500507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Aus d. Russ. übers. - Literaturverz. S. 297 - 308 |
| Umfang: | XVI, 313 S. |
| ISBN: | 0792314387 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV005588900 | ||
| 003 | DE-604 | ||
| 005 | 19921016 | ||
| 007 | t| | ||
| 008 | 921009s1991 xx |||| 00||| engod | ||
| 020 | |a 0792314387 |9 0-7923-1438-7 | ||
| 035 | |a (OCoLC)246570407 | ||
| 035 | |a (DE-599)BVBBV005588900 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-91 |a DE-188 | ||
| 084 | |a MAT 587f |2 stub | ||
| 084 | |a MAT 344f |2 stub | ||
| 100 | 1 | |a Samojlenko, Anatolij M. |d 1938-2020 |e Verfasser |0 (DE-588)108416569 |4 aut | |
| 240 | 1 | 0 | |a Ėlementy matematičeskoj teorii mnogočastotnych kolebanij |
| 245 | 1 | 0 | |a Elements of the mathematical theory of multi-frequency oscillations |c by A. M. Samoilenko |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1991 | |
| 300 | |a XVI, 313 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Soviet series |v 71 | |
| 500 | |a Aus d. Russ. übers. - Literaturverz. S. 297 - 308 | ||
| 650 | 0 | 7 | |a Schwingung |0 (DE-588)4053999-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Invarianter Torus |0 (DE-588)4552037-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Schwingung |0 (DE-588)4042100-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Methode |0 (DE-588)4155620-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Schwingung |0 (DE-588)4042100-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Schwingung |0 (DE-588)4053999-4 |D s |
| 689 | 1 | 1 | |a Invarianter Torus |0 (DE-588)4552037-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Nichtlineare Schwingung |0 (DE-588)4042100-4 |D s |
| 689 | 2 | 1 | |a Mathematische Methode |0 (DE-588)4155620-3 |D s |
| 689 | 2 | |5 DE-188 | |
| 810 | 2 | |a Soviet series |t Mathematics and its applications |v 71 |w (DE-604)BV004708148 |9 71 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003500507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |n oe | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-003500507 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001 92 A 2971 |
|---|---|
| DE-BY-TUM_katkey | 565258 |
| DE-BY-TUM_location | Mag |
| DE-BY-TUM_media_number | 040001214973 |
| _version_ | 1821937793145765891 |
| adam_text | Contents
Preface xi
Introduction xiii
CHAPTER 1. Periodic and quasi periodic functions 1
1.1. The function spaces Cr(Tm) and Hr(Tm) 1
1.2. Structure of the spaces Hr(Tm). Sobolev theorems 3
1.3. Main inequalities in Hr(Tm) 7
1.4. Quasi periodic functions. The spaces C(w) 9
1.5. The spaces Hr(u) and their structure 13
1.6. First integral of a quasi periodic function 18
1.7. Spherical coordinates of a quasi periodic vector function 25
1.8. The problem on a periodic basis in E 28
1.9. Logarithm of a matrix in C (Tm). Sibuja s theorem 38
1.10. Garding s inequality 41
CHAPTER 2. Invariant sets and their stability 46
2.1. Preliminary notions and results 46
2.2. One sided invariant sets and their properties 49
2.3. Locally invariant sets. Reduction principle 56
2.4. Behaviour of an invariant set under small perturbations of the system 65
2.5. Quasi periodic motions and their closure 70
2.6. Invariance equations of a smooth manifold and the trajectory flow
on it 83
2.7. Local coordinates in a neighbourhood of a toroidal manifold. Stability
of an invariant torus 88
2.8. Recurrent motions and multi frequency oscillations 96
CHAPTER 3. Some problems of the linear theory 99
3.1. Introductory remarks and definitions 99
viii CONTENTS
3.2. Adjoint system of equations. Necessary conditions for the existence
of an invariant torus 101
3.3. Necessary conditions for the existence of an invariant torus of a
linear system with arbitrary non homogeneity in C(Tm) 106
3.4. The Green s function. Sufficient conditions for the existence of an
invariant torus 113
3.5. Conditions for the existence of an exponentially stable invariant
torus 118
3.6. Uniqueness conditions for the Green s function and the properties
of this function 124
3.7. Separatrix manifolds. Decomposition of a linear system 134
3.8. Sufficient conditions for exponential dichotomy of an invariant torus 142
3.9. Necessary conditions for an invariant torus to be exponentially
dichotomous 151
3.10. Conditions for the C^T^ block decomposability of an exponentially
dichotomous system 158
3.11. On triangulation and the relation between the C (7^,) block decom¬
posability of a linear system and the problem of the extendability
of an r frame to a periodic basis in En 169
3.12. On smoothness of an exponentially stable invariant torus .... 178
3.13. Smoothness properties of Green s functions, the invariant torus
and the decomposing transformation of an exponentially dicho¬
tomous system 188
3.14. Galerkin s method for the construction of an invariant torus . . . 194
3.15. Proof of the main inequalities for the substantiation of Galerkin s
method 203
CHAPTER 4. Perturbation theory of an invariant torus of a non¬
linear system 211
4.1. Introductory remarks. The linearization process 211
4.2. Main theorem 215
4.3. Exponential stability of an invariant torus and conditions for its
preservation under small perturbations of the system 220
4.4. Theorem on exponential attraction of motions in a neighbourhood
of an invariant torus of a system to its motions on the torus . . . 226
4.5. Exponential dichotomy of invariant torus and conditions for its pre
CONTENTS ix
servation under small perturbations of the system 241
4.6. An estimate of the smallness of a perturbation and the maximal
smoothness of an invariant torus of a non linear system 258
4.7. Galerkin s method for the construction of an invariant torus of a
non linear system of equations and its linear modification .... 270
4.8. Proof of Moser s lemma 281
4.9. Invariant tori of systems of differential equations with rapidly and
slowly changing variables 285
Bibliography 297
Author index 309
Index of notation 310
Subject index 311
|
| any_adam_object | 1 |
| author | Samojlenko, Anatolij M. 1938-2020 |
| author_GND | (DE-588)108416569 |
| author_facet | Samojlenko, Anatolij M. 1938-2020 |
| author_role | aut |
| author_sort | Samojlenko, Anatolij M. 1938-2020 |
| author_variant | a m s am ams |
| building | Verbundindex |
| bvnumber | BV005588900 |
| classification_tum | MAT 587f MAT 344f |
| ctrlnum | (OCoLC)246570407 (DE-599)BVBBV005588900 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02045nam a2200493 cb4500</leader><controlfield tag="001">BV005588900</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19921016 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">921009s1991 xx |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0792314387</subfield><subfield code="9">0-7923-1438-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246570407</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV005588900</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 587f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 344f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Samojlenko, Anatolij M.</subfield><subfield code="d">1938-2020</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)108416569</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Ėlementy matematičeskoj teorii mnogočastotnych kolebanij</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elements of the mathematical theory of multi-frequency oscillations</subfield><subfield code="c">by A. M. Samoilenko</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht u.a.</subfield><subfield code="b">Kluwer</subfield><subfield code="c">1991</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 313 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics and its applications / Soviet series</subfield><subfield code="v">71</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Aus d. Russ. übers. - Literaturverz. S. 297 - 308</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Schwingung</subfield><subfield code="0">(DE-588)4053999-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Invarianter Torus</subfield><subfield code="0">(DE-588)4552037-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Schwingung</subfield><subfield code="0">(DE-588)4042100-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Methode</subfield><subfield code="0">(DE-588)4155620-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare Schwingung</subfield><subfield code="0">(DE-588)4042100-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Schwingung</subfield><subfield code="0">(DE-588)4053999-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Invarianter Torus</subfield><subfield code="0">(DE-588)4552037-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Nichtlineare Schwingung</subfield><subfield code="0">(DE-588)4042100-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Mathematische Methode</subfield><subfield code="0">(DE-588)4155620-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-188</subfield></datafield><datafield tag="810" ind1="2" ind2=" "><subfield code="a">Soviet series</subfield><subfield code="t">Mathematics and its applications</subfield><subfield code="v">71</subfield><subfield code="w">(DE-604)BV004708148</subfield><subfield code="9">71</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003500507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="n">oe</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-003500507</subfield></datafield></record></collection> |
| id | DE-604.BV005588900 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T08:35:44Z |
| institution | BVB |
| isbn | 0792314387 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003500507 |
| oclc_num | 246570407 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-188 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-188 |
| physical | XVI, 313 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spellingShingle | Samojlenko, Anatolij M. 1938-2020 Elements of the mathematical theory of multi-frequency oscillations Schwingung (DE-588)4053999-4 gnd Invarianter Torus (DE-588)4552037-9 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4053999-4 (DE-588)4552037-9 (DE-588)4042100-4 (DE-588)4155620-3 |
| title | Elements of the mathematical theory of multi-frequency oscillations |
| title_alt | Ėlementy matematičeskoj teorii mnogočastotnych kolebanij |
| title_auth | Elements of the mathematical theory of multi-frequency oscillations |
| title_exact_search | Elements of the mathematical theory of multi-frequency oscillations |
| title_full | Elements of the mathematical theory of multi-frequency oscillations by A. M. Samoilenko |
| title_fullStr | Elements of the mathematical theory of multi-frequency oscillations by A. M. Samoilenko |
| title_full_unstemmed | Elements of the mathematical theory of multi-frequency oscillations by A. M. Samoilenko |
| title_short | Elements of the mathematical theory of multi-frequency oscillations |
| title_sort | elements of the mathematical theory of multi frequency oscillations |
| topic | Schwingung (DE-588)4053999-4 gnd Invarianter Torus (DE-588)4552037-9 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Schwingung Invarianter Torus Nichtlineare Schwingung Mathematische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003500507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
| work_keys_str_mv | AT samojlenkoanatolijm elementymatematiceskojteoriimnogocastotnychkolebanij AT samojlenkoanatolijm elementsofthemathematicaltheoryofmultifrequencyoscillations |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Bibliotheksmagazin
| Signatur: |
0001 92 A 2971
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |