Dynamical Systems
An International Symposium
- 1st Edition - January 1, 1976
- Imprint: Academic Press
- Editors: Lamberto Cesari, Jack K. Hale, Joseph P. LaSalle
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 7 1 0 - 7
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 5 9 6 9 - 7
Dynamical Systems: An International Symposium, Volume 2 contains the proceedings of the International Symposium on Dynamical Systemsheld at Brown University in Providence, Rhode… Read more
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Request a sales quoteDynamical Systems: An International Symposium, Volume 2 contains the proceedings of the International Symposium on Dynamical Systemsheld at Brown University in Providence, Rhode Island, on August 12-16, 1974. The symposium provided a forum for reviewing the theory of dynamical systems in relation to ordinary and functional differential equations, as well as the influence of this approach and the techniques of ordinary differential equations on research concerning certain types of partial differential equations and evolutionary equations in general. Comprised of six chapters, this volume first examines how the theory of isolating blocks may be applied to the Newtonian planar three-body problem. The reader is then introduced to the separatrix structure for regions attracted to solitary periodic solutions; solitary invariant sets; and singular points and separatrices. Subsequent chapters focus on the equivalence of suspensions and manifolds with cross section; a geometrical approach to classical mechanics; bifurcation theory for odd potential operators; and continuous dependence of fixed points of condensing maps. This monograph will be of interest to students and practitioners in the field of applied mathematics.
List of Contributors
Preface
Contents of Volume 1
Chapter 1 Qualitative Theory
Some Qualitative Aspects of the Three-Body Flow
Separatrix Structure for Regions Attracted to Solitary Periodic Solutions
Solitary Invariant Sets
Singular Points and Separatrices
Global Results by Local Averaging for Nearly Hamiltonian Systems
Equivalence of Suspensions and Manifolds with Cross Section
Structural Stability Theorems
Numerical Studies of an Area-Preserving Mapping
A Geometrical Approach to Classical Mechanics
Chapter 2 General Theory
A Solution of Ulam's Conjecture on the Existence of Invariant Measures and Its Applications
Bifurcation Theory for Odd Potential Operators
An Existence Theorem for Solutions of Orientor Fields
Nonlinear Perturbations at Resonance
On Continuous Dependence of Fixed Points of Condensing Maps
Small Noise Ergodic Dynamical Systems
Chapter 3 Evolutionary Equations
"Pointwise Degeneracy" for Delay Evolutionary Equations
On Constructing a Liapunov Functional While Defining a Linear Dynamical System
Measurability and Continuity Conditions for Evolutionary Processes
Stabilization of Linear Evolutionary Processes
Chapter 4 Functional Differential Equations
Bifurcation Theory and Periodic Solutions of Some Autonomous Functional Differential Equations
A Stability Criterion for Linear Autonomous Functional Differential Equations
Periodic Differential Difference Equations
Point Data Problems for Functional Differential Equations
Relations Between Functional and Ordinary Differential Equations
Asymptotically Autonomous Neutral Functional Differential Equations with Time-Dependent Lag
The Invariance Principle for Functional Equations
Existence and Stability of Periodic Solutions of x' (t)= -f(x(t), x(t - 1)
Existence and Stability of Solutions on the Real Line to x(t) + ∫t-∞a(t – τ)g,(τ, x(τ)) dτ = (f(t), with General Forcing Term
Existence and Stability for Partial Functional Differential Equations
Periodic Solutions to a Population Equation
Existence and Stability of Forced Oscillation in Retarded Equations
Exact Solutions of Some Functional Differential Equations
Chapter 5 Topological Dynamical Systems
Extendability of an Elementary Dynamical System to an Abstract Local Dynamical System
Skew-Product Dynamical Systems
Liapunov Functions and the Comparison Principle
Distal Semidynamical Systems
Prolongations in Semidynamical Systems
When Do Liapunov Functions Exist on Invariant Neighborhoods?
The "Simplest" Dynamical System
Continuous Operators That Generate Many Flows
Existence and Continuity of Liapunov Functions in General Systems
Chapter 6 Ordinary Differential and Volterra Equations
Stability Under the Perturbation by a Class of Functions
On a General Type of Second-Order Forced Nonlinear Oscillations
Stability of Periodic Linear Systems and the Geometry of Lie Groups
Periodic Solutions of Holomorphic Differential Equations
On the Newton Method of Solving Problems of the Least Squares Type for Ordinary Differential Equations
A Study on Generation of Nonuniqueness
Relative Asymptotic Equivalence with Weight tμ , Between Two Systems of Ordinary Differential Equations
Partial Peeling
Boundary Value Problems for Perturbed Differential Equations
On Stability of Solutions of Perturbed Differential Equations
Stability Theory for Nonautonomous Systems
A Nonoscillation Result for a Forced Second-Order Nonlinear Differential Equation
Convexity Properties and Bounds for a Class of Linear Autonomous Mechanical Systems
Dynamical Systems Arising from Electrical Networks
An Invariance Principle for Vector Liapunov Functions
Stability of a Nonlinear Volterra Equation
On a Class of Volterra Integrodlfferential Equations
Existence and Continuation Properties of Solutions of a Nonlinear Volterra Integral Equation
Author Index
Subject Index
- Edition: 1
- Published: January 1, 1976
- No. of pages (eBook): 336
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9781483237107
- eBook ISBN: 9781483259697
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