Stability theory of dynamical systems:
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| Previous Title: | Grundlehren der mathematischen Wissenschaften, Vol. 161 |
|---|---|
| Main Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Edition: | Reprint of the 1970 ed. |
| Series: | Classics in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Ursprüngl. als: Grundlehren der mathematischen Wissenschaften, Vol. 161 |
| Physical Description: | XI, 225 S. graph. Darst. |
| ISBN: | 3540427481 |
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Record in the Search Index
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| adam_text | N.RBHATIA * G.P.SZEGOE STABILITYTHEORY OFDYNAMICAL SYSTEMS REPRINTOFTHE
1970 EDITION SPRINGER CONTENTS NOTATION X INTRODUCTION 1 I. DYNAMICAL
SYSTEMS 5 1. DEFINITION AND RELATED NOTATION 5 2. EXAMPLES OF DYNAMICAL
SYSTEMS 6 NOTES AND REFERENCES 10 II. ELEMENTARY CONCEPTS 12 1.
INVARIANT SETS AND TRAJECTORIES 12 2. CRITICAL POINTS AND PERIODIC
POINTS 15 3. TRAJECTORY CLOSURES AND LIMIT SETS 19 4. THE FIRST
PROLONGATION AND THE PROLONGATIONAL LIMIT SET 24 NOTES AND REFERENCES 30
III. RECURSIVE CONCEPTS. 31 1. DEFINITION OF RECURSIVENESS 31 2. POISSON
STABLE AND NON-WANDERING POINTS 31 3. MINIMAL SETS AND RECURRENT POINTS
36 4. LAGRANGE STABILITY AND EXISTENCE OF MINIMAL SETS 41 NOTES AND
REFERENCES 42 IV. DISPERSIVECONCEPTS 43 1. UNSTABLE AND DISPERSIVE
DYNAMICAL SYSTEMS 43 2. PARALLELIZABLE DYNAMICAL SYSTEMS 48 NOTES AND
REFERENCES 55 V. STABILITY THEORY 56 1. STABILITY AND ATTRACTION FOR
COMPACT SETS 56 2. LIAPUNOV FUNCTIONS: CHARACTERIZATION OF ASYMPTOTIC
STABILITY . . . 66 3. TOPOLOGICAL PROPERTIES OF REGIONS OF ATTRACTION 79
4. STABILITY AND ASYMPTOTIC STABILITY OF CLOSED SETS 84 5. RELATIVE
STABILITY PROPERTIES 99 6. STABILITY OF A MOTION AND ALMOST PERIODIC
MOTIONS 106 NOTES AND REFERENCES 111 V . FLOW NEAR A COMPACT INVARIANT
SET 114 1. DESCRIPTION OF FLOW NEAR A COMPACT INVARIANT SET 114 2. FLOW
NEAR A COMPACT INVARIANT SET (CONTINUED) 116 NOTES AND REFERENCES 117
CONTENTS IX VII. HIGHER PROLONGAT IONS 119 1. DEFINITION OF HIGHER
PROLONGATIONS 120 2. ABSOLUTE STABILITY 124 3. GENERALIZED RECURRENCE
129 NOTES AND REFERENCES 133 VIII. G 1 -LIAPUNOV FUNCTIONS FOR ORDINARY
DIFFERENTIAL EQUATIONS 134 1. INTRODUCTION 134 2. PRELIMINARY
DEFINITIONS AND PROPERTIES 136 3. LOCAL THEOREMS 138 4. EXTENSION
THEOREMS 145 5. THE STRUCTURE OF LIAPUNOV FUNCTIONS 150 6. THEOREMS
REQUIRING SEMIDEFINITE DERIVATIVES 156 7. ON THE USE OF HIGHER
DERIVATIVES OF A LIAPUNOV FUNCTION . . . 160 NOTES AND REFERENCES 162
IX. NON-CONTINU OUS LIAPUNOV FUNCTIONS FOR ORDINARY DIFFERENTIAL
EQUATIONS 166 1. INTRODUCTION 166 2. A CHARACTERIZATION OF WEAK
ATTRACTORS 169 3. PIECEWISE DIFFERENTIABLE LIAPUNOV FUNCTIONS 172 4.
LOCAL RESULTS 176 5. EXTENSION THEOREMS 177 6. NON-CONTINUOUS LIAPUNOV
FUNCTIONS ON THE REGION OF WEAK ATTRAC- TION 179 NOTES AND REFERENCES
183 REFERENCES 185 AUTHOR INDEX 221 SUBJECT INDEX 223
|
| any_adam_object | 1 |
| author | Bhatia, Nam Parshad 1932- Szegö, Giorgio P. 1934-2020 |
| author_GND | (DE-588)123509718 (DE-588)129153249 |
| author_facet | Bhatia, Nam Parshad 1932- Szegö, Giorgio P. 1934-2020 |
| author_role | aut aut |
| author_sort | Bhatia, Nam Parshad 1932- |
| author_variant | n p b np npb g p s gp gps |
| building | Verbundindex |
| bvnumber | BV014048977 |
| classification_rvk | SK 520 |
| classification_tum | MAT 345f |
| ctrlnum | (OCoLC)440752571 (DE-599)BVBBV014048977 |
| discipline | Mathematik |
| edition | Reprint of the 1970 ed. |
| format | Book |
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| id | DE-604.BV014048977 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:56:44Z |
| institution | BVB |
| isbn | 3540427481 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009621257 |
| oclc_num | 440752571 |
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| physical | XI, 225 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Classics in mathematics |
| spelling | Bhatia, Nam Parshad 1932- Verfasser (DE-588)123509718 aut Stability theory of dynamical systems N. P. Bhatia ; G. P. Szegö Reprint of the 1970 ed. Berlin [u.a.] Springer 2002 XI, 225 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classics in mathematics Ursprüngl. als: Grundlehren der mathematischen Wissenschaften, Vol. 161 Differential equations Stability Topological dynamics Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Stabilität (DE-588)4056693-6 s DE-604 Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s Szegö, Giorgio P. 1934-2020 Verfasser (DE-588)129153249 aut Ursprüngl. als Grundlehren der mathematischen Wissenschaften, Vol. 161 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009621257&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bhatia, Nam Parshad 1932- Szegö, Giorgio P. 1934-2020 Stability theory of dynamical systems Differential equations Stability Topological dynamics Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Stabilität (DE-588)4056693-6 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4167992-1 (DE-588)4056693-6 (DE-588)4013396-5 |
| title | Stability theory of dynamical systems |
| title_auth | Stability theory of dynamical systems |
| title_exact_search | Stability theory of dynamical systems |
| title_full | Stability theory of dynamical systems N. P. Bhatia ; G. P. Szegö |
| title_fullStr | Stability theory of dynamical systems N. P. Bhatia ; G. P. Szegö |
| title_full_unstemmed | Stability theory of dynamical systems N. P. Bhatia ; G. P. Szegö |
| title_old | Grundlehren der mathematischen Wissenschaften, Vol. 161 |
| title_short | Stability theory of dynamical systems |
| title_sort | stability theory of dynamical systems |
| topic | Differential equations Stability Topological dynamics Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Stabilität (DE-588)4056693-6 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Differential equations Stability Topological dynamics Ljapunov-Stabilitätstheorie Stabilität Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009621257&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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