A Rational Interval of Rotation Numbers for Periodic Points in Certain Non-Separating Plane Continua.

Details A Rational Interval of Rotation Numbers for Periodic Points in Certain Non-Separating Plane Continua. A Rational Interval of Rotation Numbers for Periodic Points in Certain Non-Separating Plane Continua.

Jan 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt........37m&link_type=abstract

Thesis (PH.D.)--MONTANA STATE UNIVERSITY, 1995.Source: Dissertation Abstracts International, Volume: 57-03, Section: B, page: 18

Computer Science

Scientific paper

Let F be an orientation preserving homeomorphism of the plane that has a fixed point that is contained in an invariant, nonseparating continuum Lambda . If p/q is a reduced rational in the interior of the convex hull of the rotation set of Lambda about the fixed point, then there exists a q-periodic point in Lambda with rotation number p/q, provided that p/q is not the local rotation number about the fixed point and that Lambda satisfies certain technical requirements. We also show that the local rotation number is a point in the closure of the rotation set of Lambda and that if this rotation set is nondegenerate, then Lambda is indecomposable.

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