ABSOLUTE EQUIVALENCE OF EXTERIOR DIFFERENTIAL SYSTEMS.

Abstract

This paper concerns an equivalence relation first defined by E. Cartan for certain systems of ordinary differential equations. He called two systems absolutely equivalent if they had isomorphic prolongations. The author extends Cartan's definition to general exterior differential systems. Two exterior differential systems are absolutely equivalent if there exists a sequence of systems beginning with one and ending with the second in which for each adjacent pair one is a partial prolongation of its neighbor. Two kinds of numerical invariants are found, depending on the characters s sub o, s sub 1, . . ., s sub p. Using Kuranishi's infinite analytic mappings, the last non-zero integer among s sub o, s sub 1, . . . s sub p is an absolute invariant. Other absolute invariants are computed from the sequence of prolongations of a given system.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1964
Accession Number
AD0609687

Entities

People

  • Harold H. Johnson

Organizations

  • University of Washington

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Geometry
  • Mathematics
  • Personality
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra