New Proof and Extension of Sarkovskii's Theorem

Abstract

Elementary periodic orbits are introduced and are shown to obey a total order. The total ordering of the elementary periodic orbits provides the basis for the proof of Theorem (SE), the principal result of this report. Theorem (SE) is an extension of Sarkovskii's Theorem and subsumes it. Theorem (SE) incorporates the notion of E(infinity) as an infinite preorbit which is directly related to the notion of turbulence. A paper with the same title was submitted for publication in the Journal of Mathematical Analysis and Applications. Elementary periodic orbits, E(oo), Sarkovskii's Theorem, Turbulence, Periodic functions.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1994
Accession Number
ADA278347

Entities

People

  • N. P. Bhatia
  • W. O. Egerland

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Army
  • Classification
  • Engineering
  • Hierarchies
  • Inequalities
  • Intervals
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • Notation
  • Periodic Functions
  • Plastic Explosives
  • Records Management
  • Security
  • Turbulence
  • United States Military Academy

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space