Hale, Jack K.
Overview
Works:  202 works in 697 publications in 5 languages and 9,792 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree, Other, Instrumentalist, Performer, Contributor, Composer, Dedicatee, Arranger 
Classifications:  QA372, 515.35 
Publication Timeline
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Most widely held works by
Jack K Hale
Dynamics and bifurcations by
Jack K Hale(
Book
)
23 editions published between 1991 and 2012 in English and German and held by 762 WorldCat member libraries worldwide
The subject of differential and difference equations is an old and muchhonored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications with perhaps a more mature look. Many of the available books and expository narratives either require extensive mathematical preparation, or are not designed to be used as textbooks. The authors have filled this void with the present book
23 editions published between 1991 and 2012 in English and German and held by 762 WorldCat member libraries worldwide
The subject of differential and difference equations is an old and muchhonored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications with perhaps a more mature look. Many of the available books and expository narratives either require extensive mathematical preparation, or are not designed to be used as textbooks. The authors have filled this void with the present book
Studies in ordinary differential equations by
Jack K Hale(
Book
)
15 editions published in 1977 in English and Undetermined and held by 633 WorldCat member libraries worldwide
15 editions published in 1977 in English and Undetermined and held by 633 WorldCat member libraries worldwide
Methods of bifurcation theory by
ShuiNee Chow(
Book
)
31 editions published between 1981 and 1996 in English and held by 630 WorldCat member libraries worldwide
The author's primary objective in this book is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To acccomplish this objective and to make the book accessible to a wider audience, much of the relevant background material from nonlinear functional analysis and the qualitative theory of differential equations is presented in detail. Two distinct aspects of bifurcation theory are discussed  static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. Dynamic bifurcation theory is concerned with the changes that occur in the structure of the limit sets of solutions of differential equations as parameters in the vector field are varied. This second printing contains extensive corrections and revisions throughout the book
31 editions published between 1981 and 1996 in English and held by 630 WorldCat member libraries worldwide
The author's primary objective in this book is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To acccomplish this objective and to make the book accessible to a wider audience, much of the relevant background material from nonlinear functional analysis and the qualitative theory of differential equations is presented in detail. Two distinct aspects of bifurcation theory are discussed  static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. Dynamic bifurcation theory is concerned with the changes that occur in the structure of the limit sets of solutions of differential equations as parameters in the vector field are varied. This second printing contains extensive corrections and revisions throughout the book
Ordinary differential equations by
Jack K Hale(
Book
)
18 editions published in 1969 in English and Undetermined and held by 599 WorldCat member libraries worldwide
18 editions published in 1969 in English and Undetermined and held by 599 WorldCat member libraries worldwide
Functional differential equations by
Jack K Hale(
Book
)
22 editions published between 1970 and 1977 in English and Undetermined and held by 569 WorldCat member libraries worldwide
The class includes some difference equations, differentialdifference equations as well as retarded functional differential equations; that is, those systems in which the derivative of the state of the system at a given time depends only upon the state of the system for previous values of time. If the solutions of the system have enough smoothness properties, then they satisfy equations for which the derivative of the state at a given time depend both upon the state and the derivative of the state for previous values of time; that is, neutral functional differential equations. The advantage in the approach seems to be the unification that is provided as well as the fact that a geometric theory becomes more feasible
22 editions published between 1970 and 1977 in English and Undetermined and held by 569 WorldCat member libraries worldwide
The class includes some difference equations, differentialdifference equations as well as retarded functional differential equations; that is, those systems in which the derivative of the state of the system at a given time depends only upon the state of the system for previous values of time. If the solutions of the system have enough smoothness properties, then they satisfy equations for which the derivative of the state at a given time depend both upon the state and the derivative of the state for previous values of time; that is, neutral functional differential equations. The advantage in the approach seems to be the unification that is provided as well as the fact that a geometric theory becomes more feasible
Oscillations in nonlinear systems by
Jack K Hale(
Book
)
20 editions published between 1963 and 2015 in 3 languages and held by 538 WorldCat member libraries worldwide
By focusing on ordinary differential equations that contain a small parameter, this concise graduatelevel introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds. Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Part II offers extensive treatment of periodic solutions, including the general theory for periodic solutions based on the work of CesariHalelGambill, with specific examples and applications of the theory. Part III covers various aspects of almost periodic solutions, including methods of averaging and the existence of integral manifolds. An indispensable resource for engineers and mathematicians with knowledge of elementary differential equations and matrices, this text is illuminated by numerous clear examples
20 editions published between 1963 and 2015 in 3 languages and held by 538 WorldCat member libraries worldwide
By focusing on ordinary differential equations that contain a small parameter, this concise graduatelevel introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds. Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Part II offers extensive treatment of periodic solutions, including the general theory for periodic solutions based on the work of CesariHalelGambill, with specific examples and applications of the theory. Part III covers various aspects of almost periodic solutions, including methods of averaging and the existence of integral manifolds. An indispensable resource for engineers and mathematicians with knowledge of elementary differential equations and matrices, this text is illuminated by numerous clear examples
Differential equations and dynamical systems; proceedings by
Jack K Hale(
Book
)
35 editions published between 1965 and 1967 in 3 languages and held by 485 WorldCat member libraries worldwide
35 editions published between 1965 and 1967 in 3 languages and held by 485 WorldCat member libraries worldwide
Theory of functional differential equations by
Jack K Hale(
Book
)
29 editions published between 1977 and 2011 in 3 languages and held by 458 WorldCat member libraries worldwide
29 editions published between 1977 and 2011 in 3 languages and held by 458 WorldCat member libraries worldwide
Asymptotic behavior of dissipative systems by
Jack K Hale(
Book
)
21 editions published between 1988 and 2009 in 3 languages and held by 455 WorldCat member libraries worldwide
21 editions published between 1988 and 2009 in 3 languages and held by 455 WorldCat member libraries worldwide
Introduction to functional differential equations by
Jack K Hale(
Book
)
14 editions published between 1993 and 2014 in English and held by 433 WorldCat member libraries worldwide
The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977. The authors have attempted to maintain the spirit of that book and have retained approximately onethird of the material intact. One major change was a completely new presentation of linear systems (Chapter 69) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global attractors was thoroughly revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (Chapters 1,2,3,9,10). Chapter 12 is also entirely new and contains a guide to active topics of research. In the sections on supplementary remarks, the authors have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive
14 editions published between 1993 and 2014 in English and held by 433 WorldCat member libraries worldwide
The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977. The authors have attempted to maintain the spirit of that book and have retained approximately onethird of the material intact. One major change was a completely new presentation of linear systems (Chapter 69) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global attractors was thoroughly revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (Chapters 1,2,3,9,10). Chapter 12 is also entirely new and contains a guide to active topics of research. In the sections on supplementary remarks, the authors have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive
An introduction to infinite dimensional dynamical systemsgeometric theory by
Jack K Hale(
Book
)
18 editions published between 1983 and 1984 in English and German and held by 413 WorldCat member libraries worldwide
18 editions published between 1983 and 1984 in English and German and held by 413 WorldCat member libraries worldwide
Dynamical systems : an international symposium : [proceedings] by
Lamberto Cesari(
Book
)
31 editions published between 1976 and 2014 in English and Italian and held by 374 WorldCat member libraries worldwide
Contents: Qualitative theory; General theory; Evolutionary equations; Functional differential equations; Topological dynamical systems; Ordinary differential and Volterra equations
31 editions published between 1976 and 2014 in English and Italian and held by 374 WorldCat member libraries worldwide
Contents: Qualitative theory; General theory; Evolutionary equations; Functional differential equations; Topological dynamical systems; Ordinary differential and Volterra equations
Topics in dynamic bifurcation theory by
Jack K Hale(
Book
)
15 editions published between 1980 and 1981 in English and held by 352 WorldCat member libraries worldwide
This set of lectures has two primary objectives. The first one is to present the general theory of first order bifurcation that occur for vector fields in finite dimensional space. Illustrations are given of higher order bifurcations. The second objective, and probably the most important one, is to set up a framework for the discussion of similar problems in infinite dimensions. Parabolic systems and retarded functional differential equations are considered as illustrations and motivations for the general theory. Readers familiar with ordinary differential equations and basic elements of nonli
15 editions published between 1980 and 1981 in English and held by 352 WorldCat member libraries worldwide
This set of lectures has two primary objectives. The first one is to present the general theory of first order bifurcation that occur for vector fields in finite dimensional space. Illustrations are given of higher order bifurcations. The second objective, and probably the most important one, is to set up a framework for the discussion of similar problems in infinite dimensions. Parabolic systems and retarded functional differential equations are considered as illustrations and motivations for the general theory. Readers familiar with ordinary differential equations and basic elements of nonli
Dynamics in infinite dimensions by
Jack K Hale(
Book
)
23 editions published between 2002 and 2010 in English and held by 265 WorldCat member libraries worldwide
This book presents aspects of a geometric theory of infinite dimensional spaces with major emphasis on retarded functional differential equations. It contains results on MorseSmale systems for semiflows, persistence of hyperbolicity under perturbations, nonuniform hyperbolicity, monotone dynamical systems, realization of vector fields on center manifolds and normal forms
23 editions published between 2002 and 2010 in English and held by 265 WorldCat member libraries worldwide
This book presents aspects of a geometric theory of infinite dimensional spaces with major emphasis on retarded functional differential equations. It contains results on MorseSmale systems for semiflows, persistence of hyperbolicity under perturbations, nonuniform hyperbolicity, monotone dynamical systems, realization of vector fields on center manifolds and normal forms
Oscillation and dynamics in delay equations : proceedings of an AMS special session held January 1619, 1991 by AMS Special session on oscillation dynamics in delay equations(
Book
)
9 editions published in 1992 in English and held by 228 WorldCat member libraries worldwide
9 editions published in 1992 in English and held by 228 WorldCat member libraries worldwide
Ordinary differential equations by
Jack K Hale(
Book
)
19 editions published between 1969 and 2009 in 3 languages and held by 211 WorldCat member libraries worldwide
Ordinary Differential Equations emphasizes the theory of nonlinear equations. The material is presented so that the reader can prepare himself for intelligent study of the current literature and for research in differential equations. A great deal of space has been devoted to specific analytical methods that are presently widely used in the applications. The global theory of twodimensional systems is presented early in the book in order to bring out the geometric properties of solutions and to help the student develop intuition. Linear systems then arise naturally in discussing the behavior of solutions near an equilibrium point. For higher order systems, a local theory near other simple in variant sets is also given. The techniques developed are then applied to stability theory and nonlinear oscillations. Chapters on bifurcation and Liapunov functions are included. (Author)
19 editions published between 1969 and 2009 in 3 languages and held by 211 WorldCat member libraries worldwide
Ordinary Differential Equations emphasizes the theory of nonlinear equations. The material is presented so that the reader can prepare himself for intelligent study of the current literature and for research in differential equations. A great deal of space has been devoted to specific analytical methods that are presently widely used in the applications. The global theory of twodimensional systems is presented early in the book in order to bring out the geometric properties of solutions and to help the student develop intuition. Linear systems then arise naturally in discussing the behavior of solutions near an equilibrium point. For higher order systems, a local theory near other simple in variant sets is also given. The techniques developed are then applied to stability theory and nonlinear oscillations. Chapters on bifurcation and Liapunov functions are included. (Author)
Nonlinear differential equations by
Jack K Hale(
Book
)
14 editions published in 1985 in English and Undetermined and held by 210 WorldCat member libraries worldwide
14 editions published in 1985 in English and Undetermined and held by 210 WorldCat member libraries worldwide
A class of functional equations of neutral type by
Jack K Hale(
Book
)
14 editions published in 1967 in English and Italian and held by 192 WorldCat member libraries worldwide
14 editions published in 1967 in English and Italian and held by 192 WorldCat member libraries worldwide
Partial differential equations by
Joseph Wiener(
Book
)
10 editions published in 1992 in English and held by 184 WorldCat member libraries worldwide
10 editions published in 1992 in English and held by 184 WorldCat member libraries worldwide
Dynamics of infinite dimensional systems by
ShuiNee Chow(
Book
)
13 editions published between 1986 and 1987 in English and Undetermined and held by 167 WorldCat member libraries worldwide
This volume presents the results of a NATO Advanced Study Institute on Dynamics of Infinite Dimensional Systems, held at the Instituto Superior Tecnico, Lisbon, Portugal, May 1924, 1986. In recent years several research workers have considered partial differential equations and functional differential equations as dynamical systems on function spaces. Such approaches have led to the formulation of more theoretical problems that need to be investigated. In the applications, the theoretical ideas have contributed significantly to a better understanding of phenomena that have been experimentally and computationally observed. The investigators of this development come from different backgrounds  some from classical partial differential equations, some from classical ordinary differential equations and some interested in specific applications. Each group has special ideas and often these ideas have not been transmitted from one group to another. The purpose of this NATO Institute was to bring together research workers from these various areas. It provided a soundboard for the impact of the ideas of each respective discipline
13 editions published between 1986 and 1987 in English and Undetermined and held by 167 WorldCat member libraries worldwide
This volume presents the results of a NATO Advanced Study Institute on Dynamics of Infinite Dimensional Systems, held at the Instituto Superior Tecnico, Lisbon, Portugal, May 1924, 1986. In recent years several research workers have considered partial differential equations and functional differential equations as dynamical systems on function spaces. Such approaches have led to the formulation of more theoretical problems that need to be investigated. In the applications, the theoretical ideas have contributed significantly to a better understanding of phenomena that have been experimentally and computationally observed. The investigators of this development come from different backgrounds  some from classical partial differential equations, some from classical ordinary differential equations and some interested in specific applications. Each group has special ideas and often these ideas have not been transmitted from one group to another. The purpose of this NATO Institute was to bring together research workers from these various areas. It provided a soundboard for the impact of the ideas of each respective discipline
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Related Identities
 Oliva, Waldyr M. Honoree
 Magalhães, Luis T.
 LaSalle, Joseph P. Other Author Editor
 Koçak, Hüseyin Author
 Chow, ShuiNee Author
 Antosiewicz, Henry A. (Henry Albert) 19252004
 Verduyn Lunel, S. M. (Sjoerd M.)
 Cesari, Lamberto Author Editor
 United States Air Force Office of Scientific Research
 Wiener, Joseph Other Author Editor
Useful Links
Associated Subjects
Bifurcation theory Canada Delay differential equations Differentiable dynamical systems Differentialdifference equations Differential equations Differential equations, Nonlinear Differential equations, Partial Differential equations, PartialAsymptotic theory Differential equationsAsymptotic theory Dynamics Engineering Functional differential equations Functional equations Global analysis (Mathematics) Global differential geometry Manifolds (Mathematics) Mathematical physics Mathematics Nonlinear mechanics Nonlinear oscillations Numerical analysis Oscillations Physics Scientists Seri dinamika Stability Topological dynamics United States
Alternative Names
Chejl, Dž 1928
Chejl, Dž. 19282009
Hale, J.
Hale, J. 1928
Hale, J. 19282009
Hale, J. (Jack K.)
Hale, J. (Jack K.), 1928
Hale, J. K.
Hale, J. K. 1928
Hale, J. K. 19282009
Hale, Jack.
Hale, Jack 1928
Hale, Jack 19282009
Hale, Jack (Jack K.), 1928
Hale, Jack K.
Hale, Jack Kenneth 1928
Hale, Jack Kenneth 19282009
Hejl, Dž.
Hejl, Džek K.
Jack K. Hale Amerikaans wiskundige (19282009)
Jack K. Hale mathématicien américain
Jack K. Hale USamerikanischer Mathematiker
Хейл, Дж 1928
Хейл, Дж. (Джек), 1928
جک هیل ریاضیدان آمریکایی
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