PageHeader : Funkcialaj Ekvacioj, 1 (1958), 1?50
Title : Geometric Study of Nonlinear
Title : Autonomous Oscillations
AuthorInfo : By Minoru URABE
AuthorInfo : (Hiroshima University)
section : Preface
section : CONTENTS
section : CHAPTER I MOVING ORTHONORMAL SYSTEM ALONG A CLOSED PATH
subsection : 1. 1 Continuous moving orthonormal system
subsection : 1. 2 Convenient method to construct a moving orthonormal system
subsection : 1. 3 Remarks
section : CHAPTER II VARIATION PROBLEM
subsection : 2. 1 Equations for normal variations of solutions
subsection : 2. 2 Equations for normal components of variations of solutions
subsection : 2. 3 Multipliers of solutions of the normal variational equation
subsection : 2. 4 Orbital stability
section : CHAPTER III PERTURBATION PROBLEM
subsection : 3. 1 Fundamental formulas
subsection : 3. 2 Existence of periodic solutions for the perturbed system
subsection : 3.3 Stability of a periodic solution of the perturbed system
section : CHAPTER IV PERTURBATION OF A FULLY OSCILLATORY SYSTEM
subsection : 4. 1 Existence of a continuous universal period
subsection : 4. 2 Moving orthonormal systems along closed paths
subsection : 4. 3 Existence of periodic solutions for the perturbed system
subsection : 4. 4 Stability of a periodic solution of the perturbed system
subsection : 4. 5 Remarks
section : CHAPTER V PERTURBATION OF A PARTIALLY OSCILLATORY SYSTEM
subsection : 5. 1 m-parameter family of periodic sclutions
subsection : 5. 2 Existence of periodic solutions for the perturbed system
section : CHAPTER VI TWO DIMENSIONAL AUTONOMOUS SYSTEM
subsection : 6. 1 Fundamental formulas
subsection : 6. 2 Variation problem and perturbation problem
subsection : 6. 3 Perturbation of a fully oscillatory system
subsection : Example
section : CHAPTER VII ANALYTIC TWO DIEMNSIONAL AUTONOMOUS SYSTEM
subsection : 7. 1 Fundamental formulas
subsection : 7. 2 Orbital stability
subsection : 7. 3 Perturbation problem
subsection : 7. 4 Perturbation of a fully oscillatory system
section : References