An Introduction To Stability Theory
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An Introduction To Stability Theory
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Author : Anand Pillay
language : en
Publisher: Courier Corporation
Release Date : 2013-05-17
An Introduction To Stability Theory written by Anand Pillay and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-17 with Mathematics categories.
This introductory treatment covers the basic concepts and machinery of stability theory. Lemmas, corollaries, proofs, and notes assist readers in working through and understanding the material and applications. Full of examples, theorems, propositions, and problems, it is suitable for graduate students in logic and mathematics, professional mathematicians, and computer scientists. Chapter 1 introduces the notions of definable type, heir, and coheir. A discussion of stability and order follows, along with definitions of forking that follow the approach of Lascar and Poizat, plus a consideration of forking and the definability of types. Subsequent chapters examine superstability, dividing and ranks, the relation between types and sets of indiscernibles, and further properties of stable theories. The text concludes with proofs of the theorems of Morley and Baldwin-Lachlan and an extension of dimension theory that incorporates orthogonality of types in addition to regular types.
Stability Theory
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Author : Horst Leipholz
language : en
Publisher: Springer
Release Date : 1987-03
Stability Theory written by Horst Leipholz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03 with Science categories.
There have been great advances in theory of stability in recent decades due to the requirements of control theory and flight mechanics, for example. We need only mention the theory of A. M. Lyapunov. A number of specialists have given a very mathematical and abstract description of the Lyapunov stability theory which resulted in a 'stability theory of motion' applicable to the kinetics of rigid bodies and systems. The stability theory of elastomechanics was developed independently. However, there have been a number of important developments in recent years, also with respect to this theory, dealing with the following problems: The concept of the 'follower forces', non-conservative loads, respectively, has been introduced in aeroelasticity. A number of prob lems in elastic kinetics that involve pulsating loads or periodically varying parameters has led to new stability questions. So-called 'kinetic' methods have become necessary in elastomechnics in order to determine the stability bound aries. An evaluation of the stability criteria of elastostatics, which have been assumed to be generally valid, has shown that they can only be applied to a limited number of problems under special assumptions. The transition from stability to instability is a kinetic process in elastomechanics. Therefore, the most general and most certain method of determining stability is the kinetic stability criterion even if in special cases the classical stability criteria of elastostatics may remain valid. This will be discussed in detail in Section 2. 3.
Introduction To The Theory Of Stability
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Author : David R. Merkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To The Theory Of Stability written by David R. Merkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Many books on stability theory of motion have been published in various lan guages, including English. Most of these are comprehensive monographs, with each one devoted to a separate complicated issue of the theory. Generally, the examples included in such books are very interesting from the point of view of mathematics, without necessarily having much practical value. Usually, they are written using complicated mathematical language, so that except in rare cases, their content becomes incomprehensible to engineers, researchers, students, and sometimes even to professors at technical universities. The present book deals only with those issues of stability of motion that most often are encountered in the solution of scientific and technical problems. This allows the author to explain the theory in a simple but rigorous manner without going into minute details that would be of interest only to specialists. Also, using appropriate examples, he demonstrates the process of investigating the stability of motion from the formulation of a problem and obtaining the differential equations of perturbed motion to complete analysis and recommendations. About one fourth of the examples are from various areas of science and technology. Moreover, some of the examples and the problems have an independent value in that they could be applicable to the design of various mechanisms and devices. The present translation is based on the third Russian edition of 1987.
Ordinary Differential Equations And Stability Theory
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Author : David A. Sanchez
language : en
Publisher: Courier Dover Publications
Release Date : 2019-09-18
Ordinary Differential Equations And Stability Theory written by David A. Sanchez and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-18 with Mathematics categories.
This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.
Introduction To The Theory Of Stability
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Author : Evgeniĭ Alekseevich Barbashin
language : en
Publisher:
Release Date : 1970
Introduction To The Theory Of Stability written by Evgeniĭ Alekseevich Barbashin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Differential equations categories.
Stability Theory
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Author : Horst Leipholz
language : en
Publisher:
Release Date : 1970
Stability Theory written by Horst Leipholz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Stability categories.
Stability Theory
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Author : Horst H. E. Leipholz
language : en
Publisher: New York : Academic Press
Release Date : 1970
Stability Theory written by Horst H. E. Leipholz and has been published by New York : Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Science categories.
Stability Theory And The Existence Of Periodic Solutions And Almost Periodic Solutions
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Author : T. Yoshizawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stability Theory And The Existence Of Periodic Solutions And Almost Periodic Solutions written by T. Yoshizawa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Since there are several excellent books on stability theory, the author selected some recent topics in stability theory which are related to existence theorems for periodic solutions and for almost periodic solutions. The author hopes that these notes will also serve as an introduction to stability theory. These notes contain stability theory by Liapunov's second method and somewhat extended discussion of stability properties in almost periodic systems, and the existence of a periodic solution in a periodic system is discussed in connection with the boundedness of solutions, and the existence of an almost periodic solution in an almost periodic system is considered in con nection with some stability property of a bounded solution. In the theory of almost periodic systems, one has to consider almost periodic functions depending on parameters, but most of text books on almost periodic functions do not contain this case. Therefore, as mathemati cal preliminaries, the first chapter is intended to provide a guide for some properties of almost periodic functions with parameters as well as for properties of asymptotically almost periodic functions. These notes originate from a seminar on stability theory given by the author at the Mathematics Department of Michigan State Univer sity during the academic year 1972-1973. The author is very grateful to Professor Pui-Kei Wong and members of the Department for their warm hospitality and many helpful conversations. The author wishes to thank Mrs.
An Introduction To Stability Theory Of Dynamical Systems
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Author : Stephen Laurel Schey
language : en
Publisher:
Release Date : 1973
An Introduction To Stability Theory Of Dynamical Systems written by Stephen Laurel Schey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.
The thesis investigates stable, asymptotically stable and unstable dynamical systems from a topological point of view with direct application and interpretation to systems of differential equations. Knowledge of topology is not a prerequisite. Specifically, such concepts as Poisson and Liapunov stability as well as parallelizable and dispersive systems are investigated. (Author).
Stability Theory Of Dynamical Systems
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Author : N.P. Bhatia
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-10
Stability Theory Of Dynamical Systems written by N.P. Bhatia and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-10 with Science categories.
Reprint of classic reference work. Over 400 books have been published in the series Classics in Mathematics, many remain standard references for their subject. All books in this series are reissued in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. "... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well-written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."