Perturbation Methods in Non-Linear Systems

1. Front Matter

   Pages i-ix

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2. Introduction

   • Georgio Eugenio Oscare Giacaglia

   Pages 1-7

3. Canonical Transformation Theory and Generalizations

   • Georgio Eugenio Oscare Giacaglia

   Pages 8-54

4. Perturbation Methods for Hamiltonian Systems. Generalizations

   • Georgio Eugenio Oscare Giacaglia

   Pages 55-153

5. Perturbations of Integrable Systems

   • Georgio Eugenio Oscare Giacaglia

   Pages 154-208

6. Perturbations of Area Preserving Mappings

   • Georgio Eugenio Oscare Giacaglia

   Pages 209-273

7. Resonance

   • Georgio Eugenio Oscare Giacaglia

   Pages 274-354

8. Back Matter

   Pages 355-369

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This volume is intended to provide a comprehensive treatment of recent developments in methods of perturbation for nonlinear systems of ordinary differ­ ential equations. In this respect, it appears to be a unique work. The main goal is to describe perturbation techniques, discuss their ad­ vantages and limitations and give some examples. The approach is founded on analytical and numerical methods of nonlinear mechanics. Attention has been given to the extension of methods to high orders of approximation, required now by the increased accuracy of measurements in all fields of science and technology. The main theorems relevant to each perturbation technique are outlined, but they only provide a foundation and are not the objective of these notes. Each chapter concludes with a detailed survey of the pertinent literature, supplemental information and more examples to complement the text, when necessary, for better comprehension. The references are intended to provide a guide for background information and for the reader who wishes to analyze any particular point in more detail. The main sources referenced are in the fields of differential equations, nonlinear oscillations and celestial mechanics. Thanks are due to Katherine MacDougall and Sandra Spinacci for their patience and competence in typing these notes. Partial support from the Mathematics Program of the Office of Naval Research is gratefully acknowledged.

• Lie
• Perturbation
• equation
• mathematics
• theorem
• variable

• University of Sao Paulo, Brazil

  Georgio Eugenio Oscare Giacaglia

• University of Texas at Austin, USA

  Georgio Eugenio Oscare Giacaglia

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