Analysis of Dynamical Systems

Abstract

Hale and Lin have studied extensively the problem of transverse homoclinic orbits of periodic orbits of functional differential equations (FDE's). They have shown that the classical symbolic dynamics for such problems in finite dimension also holds for FDE's (Hale and Lin). These results were applied to two examples that had previously been cindifered by Walther and an der Heiden (Hale and Lin 2). For these examples, it was a transverse homoclinic orbit to a periodic orbit and, thus chaos occurs and is persistent under perturbations of thr vector field. The latter important property could be obtained by the methods of Walther and an der Heiden.

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Document Details

Document Type
Technical Report
Publication Date
Aug 24, 1988
Accession Number
ADA204636

Entities

People

  • Jack K. Hale

Organizations

  • Brown University

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Boundaries
  • Classification
  • Coefficients
  • Differential Equations
  • Diffusion
  • Diffusion Coefficient
  • Diffusivity
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Perturbations
  • Security
  • Transverse

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Snow Cover Descriptors for Reptiles and Their Illustrations.

Technology Areas

  • Space
  • Space - Orbital Debris
  • Space - Satellites