Dynamic systems on measure chains:
Dynamic Systems on Measure Chains presents the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on the times scales. In chapter two, dyn...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1996
|
| Series: | Mathematics and its applications
370 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Dynamic Systems on Measure Chains presents the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on the times scales. In chapter two, dynamic systems on time scales are introduced, and the basic properties of solutions of such dynamic systems are proven. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. The readership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets. |
| Physical Description: | X, 285 S. |
| ISBN: | 0792341163 |
Staff View
MARC
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| 490 | 1 | |a Mathematics and its applications |v 370 | |
| 520 | 3 | |a Dynamic Systems on Measure Chains presents the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on the times scales. In chapter two, dynamic systems on time scales are introduced, and the basic properties of solutions of such dynamic systems are proven. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. The readership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets. | |
| 650 | 7 | |a Dynamique différentiable |2 ram | |
| 650 | 7 | |a Équations aux différences |2 ram | |
| 650 | 4 | |a Difference equations | |
| 650 | 4 | |a Differentiable dynamical systems | |
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Record in the Search Index
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| adam_text |
TABLE OF CONTENTS
Preface vii
Chapter 1 1
1.0 Introduction 1
1.1 Measure chains and time scales 3
1.2 Differentiation 11
1.3 Mean value theorem and consequences 19
1.4 Integral and antiderivative 28
1.5 Notes 37
Chapter 2 39
2.0 Introduction 39
2.1 Local existence and uniqueness 40
2.2 Dynamic inequalities 46
2.3 Existence of extremal solutions 52
2.4 Comparison results 54
2.5 Linear variation of parameters 59
2.6 Continuous dependence 62
vi
2.7 Nonlinear variation of parameters 68
2.8 Global existence and stability 75
2.9 Notes 79
Chapter 3 81
3.0 Introduction 81
3.1 Comparison theorems 82
3.2 Stability criteria 90
3.3 A technique in stability theory 99
3.4 Stability of conditionally invariant sets 102
3.5 Stability in terms of two measures 121
3.6 Vector Lyapunov functions and practical stability 131
3.7 Notes 140
Chapter 4 143
4.0 Introduction 143
4.1 Monotone iterative technique 144
4.2 Method of quasilinearization 162
4.3 Monotone flows and stationary points 175
4.4 Invariant manifolds 189
4.5 Practical stability of large scale
uncertain dynamic systems 200
4.6 Boundary value problems 211
4.7 Sturmian theory 221
4.8 Convexity of solutions relative to the initial data 258
4.9 Invariance principle 264
4.10 Notes 273
References 275
Subject Index 283 |
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| id | DE-604.BV011070911 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-17T09:01:11Z |
| institution | BVB |
| isbn | 0792341163 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007415481 |
| oclc_num | 34789831 |
| open_access_boolean | |
| owner | DE-12 DE-384 |
| owner_facet | DE-12 DE-384 |
| physical | X, 285 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Lakshmikantham, Vangipuram 1926-2012 Verfasser (DE-588)104268050 aut Dynamic systems on measure chains by V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan Dordrecht [u.a.] Kluwer Acad. Publ. 1996 X, 285 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 370 Dynamic Systems on Measure Chains presents the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on the times scales. In chapter two, dynamic systems on time scales are introduced, and the basic properties of solutions of such dynamic systems are proven. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. The readership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets. Dynamique différentiable ram Équations aux différences ram Difference equations Differentiable dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s DE-604 Sivasundaram, S. Verfasser aut Kaymakcalan, B. Verfasser aut Mathematics and its applications 370 (DE-604)BV008163334 370 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007415481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lakshmikantham, Vangipuram 1926-2012 Sivasundaram, S. Kaymakcalan, B. Dynamic systems on measure chains Mathematics and its applications Dynamique différentiable ram Équations aux différences ram Difference equations Differentiable dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4137931-7 |
| title | Dynamic systems on measure chains |
| title_auth | Dynamic systems on measure chains |
| title_exact_search | Dynamic systems on measure chains |
| title_full | Dynamic systems on measure chains by V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan |
| title_fullStr | Dynamic systems on measure chains by V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan |
| title_full_unstemmed | Dynamic systems on measure chains by V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan |
| title_short | Dynamic systems on measure chains |
| title_sort | dynamic systems on measure chains |
| topic | Dynamique différentiable ram Équations aux différences ram Difference equations Differentiable dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Dynamique différentiable Équations aux différences Difference equations Differentiable dynamical systems Differenzierbares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007415481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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