Accession Number:

ADA278347

Title:

New Proof and Extension of Sarkovskii's Theorem

Descriptive Note:

Final rept. May 1991-May 1993

Corporate Author:

ARMY RESEARCH LAB ABERDEEN PROVING GROUND MD

Personal Author(s):

• Bhatia, N. P.
• Egerland, W. O.

Report Date:

1994-02-01

Pagination or Media Count:

23.0

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 Sarkovskiis Theorem and subsumes it. Theorem SE incorporates the notion of Einfinity 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, Eoo, Sarkovskiis Theorem, Turbulence, Periodic functions.

Descriptors:

• *ITERATIONS
• *PERIODIC FUNCTIONS
• ORBITS
• CHAOS
• TURBULENCE
• POINTS(MATHEMATICS)
• SEQUENCES(MATHEMATICS)
• ORDER DISORDER TRANSFORMATIONS
• PERTURBATION THEORY

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE