Accession Number:

ADA149875

Title:

Resonance Zones in Two-Parameter Families of Circle Homeomorphisms,

Descriptive Note:

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1984-11-01

Pagination or Media Count:

8.0

Abstract:

We consider a two-parameter family of diffeomorphisms of the circle where one of the parameters controls the amount of rigid rotation while the second controls the nonlinearity. In particular, we show that the regions in the parameter plane for which the map has a periodic orbit of a particular rotation number resonance zones increase in size linearly as the second parameter is increased from zero. This is a discretization of the phenomenon known as phase locking for ordinary differential equations. Using this, we obtain some results on the smoothness of the curves between the resonance zones. Originator-supplied key words include periodic orbits, resonance, phase locking. Author.

Subject Categories:

  • Numerical Mathematics
  • Acoustics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE