ANALYTIC TWO-DIMENSIONAL SUBCENTER MANIFOLDS FOR SYSTEMS WITH AN INTEGRAL

Abstract

For a real analytic system of ordinary differential equations with an integral H = lambda/2(x squared + y squared) + F(z) + G(x,y,z); x dot = lambda y + X(x,y,z); y dot = - lambda x + Y(x,y,z); z dot = Bz + Z(x,y,z) where x and y are scalars; z is an m-vector; X, Y, Z are power series with no constant or linear terms; B is a constant matrix with eigenvalues Mu sub 1, ..., mu sub m and i mu sub j/lambda is not equal to an integer (j = 1, ..., m) the existence of a unique, local, real analytic, two-dimensional, invariant subcenter manifold is proved.

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Document Details

Document Type
Technical Report
Publication Date
May 10, 1968
Accession Number
AD0697230

Entities

People

  • Al Kelley

Organizations

  • University of California, Santa Cruz

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analytic Functions
  • Coefficients
  • Complex Numbers
  • Complex Variables
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Equations
  • Integrals
  • Mathematics
  • Numbers
  • Power Series
  • Real Numbers
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Linear Algebra