Asymptotic solutions of strongly nonlinear systems of differential equations:
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | 1 Online-Ressource (270 S.) 2 schw.-w. Ill. |
| ISBN: | 364233816X 9783642338175 |
| DOI: | 10.1007/978-3-642-33817-5 |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
1 SEMI-QUASIHOMOGENEOUS SYSTEMS O F DIFFERENTIAL EQUATIONS 1
1.1 FORMAL ASYMPTOTIC PARTICULAR SOLUTIONS O F SEMIQUASIHOMOGENEOUS
SYSTEMS O F DIFFERENTIAL EQUATIONS 1
1.2 PROBLEMS O F CONVERGENCE 13
1.3 EXPONENTIAL METHODS FOR FINDING NONEXPONENTIAL SOLUTIONS 24
1.4 EXAMPLES 41
1.5 GROUP THEORETICAL INTERPRETATION 55
2 THE CRITICAL CASE O F PURE IMAGINARY ROOTS 77
2.1 ASYMPTOTIC SOLUTIONS O F AUTONOMOUS SYSTEMS OF DIFFERENTIAL
EQUATIONS IN THE CRITICAL CASE O F M PAIRS O F PURE IMAGINARY AND N - 2
M ZERO ROOTS O F THE CHARACTERISTIC EQUATION 77
2.2 PERIODIC AND QUASIPERIODIC SYSTEMS 92
2.3 HAMILTONIAN SYSTEMS 108
3 SINGULAR PROBLEMS 131
3.1 ASYMPTOTIC SOLUTIONS O F AUTONOMOUS SYSTEMS O F DIFFERENTIAL
EQUATIONS IN THE CRITICAL CASE O F ZERO ROOTS OF THE CHARACTERISTIC
EQUATION 131
3.2 CONCERNING ITERATED LOGARITHMS 143
3.3 SYSTEMS IMPLICIT WITH RESPECT TO HIGHER DERIVATIVES AND KUZNETSOV S
THEORY 152
4 INVERSION PROBLEM FOR THE LAGRANGE THEOREM ON THE STABILITY O F
EQUILIBRIUM AND RELATED PROBLEMS 169
4.1 ON ENERGY CRITERIA FOR STABILITY 169
4.2 REGULAR PROBLEMS 189
4.3 SINGULAR PROBLEMS 200
HTTP://D-NB.INFO/1025651278
IMAGE 2
X CONTENTS
A NONEXPONENTIAL ASYMPTOTIC SOLUTIONS O F SYSTEMS
O F FUNCTIONAL-DIFFERENTIAL EQUATIONS 215
B ARITHMETIC PROPERTIES O F THE EIGENVALUES O F THE KOVALEVSKY MATRIX
AND CONDITIONS FOR THE NONINTEGRABILITY O F SEMI-QUASIHOMOGENEOUS
SYSTEMS O F ORDINARY DIFFERENTIAL EQUATIONS 229
LITERATURE 249
INDEX 259
ASYMPTOTIC SOLUTIONS OF STRONGLY NONLINEAR SYSTEMS OF DIFFERENTIAL
EQUATIONS
/ KOZLOV, VALERY V.
: 2013
ABSTRACT / INHALTSTEXT
THE BOOK IS DEDICATED TO THE CONSTRUCTION OF PARTICULAR SOLUTIONS OF
SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS IN THE FORM OF SERIES THAT
ARE ANALOGOUS TO THOSE USED IN LYAPUNOV’S FIRST METHOD. A PROMINENT
PLACE IS GIVEN TO ASYMPTOTIC SOLUTIONS THAT TEND TO AN EQUILIBRIUM
POSITION, ESPECIALLY IN THE STRONGLY NONLINEAR CASE, WHERE THE EXISTENCE
OF SUCH SOLUTIONS CAN’T BE INFERRED ON THE BASIS OF THE FIRST
APPROXIMATION ALONE. THE BOOK IS ILLUSTRATED WITH A LARGE NUMBER OF
CONCRETE EXAMPLES OF SYSTEMS IN WHICH THE PRESENCE OF A PARTICULAR
SOLUTION OF A CERTAIN CLASS IS RELATED TO SPECIAL PROPERTIES OF THE
SYSTEM’S DYNAMIC BEHAVIOR. IT IS A BOOK FOR STUDENTS AND SPECIALISTS
WHO WORK WITH DYNAMICAL SYSTEMS IN THE FIELDS OF MECHANICS, MATHEMATICS,
AND THEORETICAL PHYSICS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Kozlov, Valerij V. Furta, Stanislav D. |
| author_facet | Kozlov, Valerij V. Furta, Stanislav D. |
| author_role | aut aut |
| author_sort | Kozlov, Valerij V. |
| author_variant | v v k vv vvk s d f sd sdf |
| building | Verbundindex |
| bvnumber | BV040805677 |
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| ctrlnum | (OCoLC)816376618 (DE-599)DNB1025651278 |
| 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 |
| doi_str_mv | 10.1007/978-3-642-33817-5 |
| format | Electronic eBook |
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| spelling | Kozlov, Valerij V. Verfasser aut Asimptotiki rešenij silʹno nelinejnych sistem differentcialʹnych uravnenij Asymptotic solutions of strongly nonlinear systems of differential equations Valery V. Kozlov ; Stanislav D. Furta Berlin [u.a.] Springer 2013 1 Online-Ressource (270 S.) 2 schw.-w. Ill. txt rdacontent c rdamedia cr rdacarrier Springer monographs in mathematics Aus dem Russ. übers. System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd rswk-swf Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 gnd rswk-swf Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd rswk-swf System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 s Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 s Asymptotisches Lösungsverhalten (DE-588)4134367-0 s DE-604 Furta, Stanislav D. Verfasser aut Erscheint auch als Druck-Ausgabe, Hardcover 978-3-642-33816-8 https://doi.org/10.1007/978-3-642-33817-5 Verlag Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025785690&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025785690&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Kozlov, Valerij V. Furta, Stanislav D. Asymptotic solutions of strongly nonlinear systems of differential equations System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd |
| subject_GND | (DE-588)4116671-1 (DE-588)4229541-5 (DE-588)4134367-0 |
| title | Asymptotic solutions of strongly nonlinear systems of differential equations |
| title_alt | Asimptotiki rešenij silʹno nelinejnych sistem differentcialʹnych uravnenij |
| title_auth | Asymptotic solutions of strongly nonlinear systems of differential equations |
| title_exact_search | Asymptotic solutions of strongly nonlinear systems of differential equations |
| title_full | Asymptotic solutions of strongly nonlinear systems of differential equations Valery V. Kozlov ; Stanislav D. Furta |
| title_fullStr | Asymptotic solutions of strongly nonlinear systems of differential equations Valery V. Kozlov ; Stanislav D. Furta |
| title_full_unstemmed | Asymptotic solutions of strongly nonlinear systems of differential equations Valery V. Kozlov ; Stanislav D. Furta |
| title_short | Asymptotic solutions of strongly nonlinear systems of differential equations |
| title_sort | asymptotic solutions of strongly nonlinear systems of differential equations |
| topic | System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 gnd Asymptotisches Lösungsverhalten (DE-588)4134367-0 gnd |
| topic_facet | System von gewöhnlichen Differentialgleichungen Nichtlineares Differentialgleichungssystem Asymptotisches Lösungsverhalten |
| url | https://doi.org/10.1007/978-3-642-33817-5 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025785690&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025785690&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kozlovvalerijv asimptotikiresenijsilʹnonelinejnychsistemdifferentcialʹnychuravnenij AT furtastanislavd asimptotikiresenijsilʹnonelinejnychsistemdifferentcialʹnychuravnenij AT kozlovvalerijv asymptoticsolutionsofstronglynonlinearsystemsofdifferentialequations AT furtastanislavd asymptoticsolutionsofstronglynonlinearsystemsofdifferentialequations |