Dynamical Systems - 1st Edition - ISBN: 9780121649029, 9781483259697

Dynamical Systems

1st Edition

An International Symposium

Editors: Lamberto Cesari Jack K. Hale Joseph P. LaSalle
eBook ISBN: 9781483259697
Imprint: Academic Press
Published Date: 1st January 1976
Page Count: 336
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Dynamical 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.

Table of Contents

List of Contributors


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


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© Academic Press 1976
Academic Press
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About the Editor

Lamberto Cesari

Jack K. Hale

Joseph P. LaSalle

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