PROOF OF MOSER'S INVARIANT CURVE THEOREM IN THE ANALYTIC CASE,

Abstract

In this report a theorem is proved establishing the existence of curves with analytic representation which are invariant under a certain analytic area preserving mapping. The mapping is a perturbation of a rotation or twist mapping and arises naturally in some undamped physical motions. This theorem modifies an invariant curve theorem proved by J. Moser to guarantee that there are 'analytic' curves invariant under the mapping and is an application of a technique for overcoming small divisors which was introduced by Kolmogorov in the study of perturbations of integrable Hamiltonian systems. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1965
Accession Number
AD0616278

Entities

People

  • Thomas Gilmer Proctor

Organizations

  • North Carolina State University

Tags

DTIC Thesaurus Topics

  • Angular Motion
  • Guarantees
  • Mathematical Analysis
  • Mathematics
  • Motion
  • Perturbations
  • Rotation

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra