Accession Number:

AD0434210

Title:

ALMOST PERIODIC SURFACES,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV BERKELEY

Personal Author(s):

Report Date:

1964-01-01

Pagination or Media Count:

33.0

Abstract:

This paper concerns systems of knm ordinary differential equations. Under suitable hypotheses a surface given by m functions of nl variables, which is made up entirely of solutions of the system as has certain stability properties exists. The functions are allowed to be almost periodic in the time variable and the resulting surface is called an almost periodic surface. It is shown that the existence of an almost periodic surface, is equivalent to ythe existence of a fixed point for a certain transformation defined on the space of parameterizing functions. Conditions under which the transformation has a fixed point are given. The methods and results are similar to those of Hale, and Bogoliubov and Mitropolski, the essential difference being that in these results the corresponding matrix is diagonal. In both cases these results are applied to more general systems. A more careful comparison of the two results is given. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE