Contributions to the Theory of Nonlinear Oscillations, Volume V

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Contributions to the Theory of Nonlinear Oscillations, Volume V

Edited by: Lamberto Cesari , J. LaSalle and Solomon Lefschetz

Language: English

Published/Copyright: 2016

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About this book

Classic contributions to the theory of nonlinear oscillations from the acclaimed Annals of Mathematics Studies series

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century.

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Mathematics Discrete Mathematics

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Frontmatter
i

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Preface
v

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Contents
vii

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I. The Time Optimal Control Problem
1
J. P. La Salle

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II. Continuous Dependence on a Parameter
25
J. Jarnik and J. Kurzweil

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III. Poincare’s Perturbation Method and Topological Degree
37
Jane Cronin

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IV. On the Behavior of the Solutions of Linear Periodic Differential Systems Near Resonance Points
55
Jack K. Hale

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V. On the Stability of Periodic Solutions of Weakly Nonlinear Periodic and Autonomous Differential Systems
91
J. K. Hale

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VI. Existence Theorems for Periodic Solutions of Nonlinear Lipschitzian Differential Systems and Fixed Point Theorems
115
Lamberto Cesari

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VII. The Applications of a Fixed Point Theorem to a Variety of Non-Linear Stability Problems
173
Arnold Stokes

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VIII. Quadratic Differential Equations and Non-Associative Algebras
185
Lawrence Markus

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IX. Sur Une Propriété De L’Ensemble Des Thajectoires Bornées De Certains Systèmes Dynamiques
215
Georges Reeb

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X. On Lagrange Stable Motions in the Neighborhood of Critical Points
219
Pinchas Mendelson

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XI. The Local Theory of Piecewise Continuous Differential Equations
225
J. André and P. Seibert

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XII. Asymptotic Stability in 3-Space
257
Courtney Coleman

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XIII. Existence and Uniqueness of the Periodic Solution of an Equation for Autonomous Oscillations
269
Rui Pacheco de Figueiredo

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Appendix
285
E. Pinney

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

June 6, 2016

eBook ISBN:

9781400882649

Pages and Images/Illustrations in book

https://doi.org/10.1515/9781400882649

eBook ISBN: 9781400882649

Keywords for this book

Theorem; Periodic function; Equation; Bifurcation theory; Characteristic exponent; Differential equation; Eigenvalues and eigenvectors; Cartesian coordinate system; Linear differential equation; Coefficient; Lipschitz continuity; Floquet theory; Existence theorem; Lyapunov stability; Special case; Degeneracy (mathematics); Elliptic function; Nonlinear system; Continuous function; Degrees of freedom (statistics); Cauchy sequence; Quadratic function; Dimensional analysis; Differentiable function; N-vector; Maxima and minima; Existential quantification; Uniqueness theorem; Quadratic differential; Characteristic polynomial; Limit cycle; Affine space; Differentiable manifold; Fixed point (mathematics); Sign (mathematics); Linear space (geometry); Parametrization; Equations of motion; Implicit function theorem; Analytic function; Determinant; Control function (econometrics); Limit point; Hypersurface; Endomorphism; Homeomorphism; Vector space; Big O notation; Linear map; Orbital stability; Linearity; Manifold; Piecewise; Complex conjugate; Dimension; Scientific notation; Submanifold; Coefficient matrix; Convex set; Linear algebra; Real projective space; Homotopy; Affine plane; Summation; Probability; Clockwise; Connected space; Optimal control; Hyperplane; Theory

Audience(s) for this book

For an expert adult audience, including professional development and academic research

Contributions to the Theory of Nonlinear Oscillations, Volume V

Overview

About this book

Topics

Table of contents

Frontmatter

Preface

Contents

I. The Time Optimal Control Problem

II. Continuous Dependence on a Parameter

III. Poincare’s Perturbation Method and Topological Degree

IV. On the Behavior of the Solutions of Linear Periodic Differential Systems Near Resonance Points

V. On the Stability of Periodic Solutions of Weakly Nonlinear Periodic and Autonomous Differential Systems

VI. Existence Theorems for Periodic Solutions of Nonlinear Lipschitzian Differential Systems and Fixed Point Theorems

VII. The Applications of a Fixed Point Theorem to a Variety of Non-Linear Stability Problems

VIII. Quadratic Differential Equations and Non-Associative Algebras

IX. Sur Une Propriété De L’Ensemble Des Thajectoires Bornées De Certains Systèmes Dynamiques

X. On Lagrange Stable Motions in the Neighborhood of Critical Points

XI. The Local Theory of Piecewise Continuous Differential Equations

XII. Asymptotic Stability in 3-Space

XIII. Existence and Uniqueness of the Periodic Solution of an Equation for Autonomous Oscillations

Appendix

Bibliographic data