Accession Number : ADA130493

Title :   Resonance Zones in Two-Parameter Families of Circle Homeomorphisms.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Hall,Glen Richard

PDF Url : ADA130493

Report Date : May 1983

Pagination or Media Count : 14

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. (Author)

Descriptors :   *Circles, Mapping, Orbits, Periodic functions, Phase locked systems, Resonance, Theorems, Differential equations

Subject Categories : Numerical Mathematics
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Distribution Statement : APPROVED FOR PUBLIC RELEASE