The Dynamics of Semigroups of Contraction Similarities on the Plane
Abstract
Consider two objects associated to the Iterated Function System (IFS) {λz + 1, λz − 1}: the locus M of parameters λ ∈ D \ {0} for which the corresponding attractor is connected; and the locus M0 of parameters for which the related attractor contains 0. The set M can also be characterized as the locus of parameters for which the attractor of the IFS {λz + 1, λz, λz − 1} contains 1/λ. Exploiting the asymptotic similarity of M and M0 with the respective associated attractors, we give sufficient conditions on λ ∈ ∂M or ∂M0 to guarantee it is accessible (not buried). Moreover, for a specific parameter λ ∈ ∂M ∩∂M0 we describe a method to show it is accessible from the connected component of D \ M containing the origin.
Degree
Ph.D.
Advisors
Pérez, Purdue University.
Subject Area
Mathematics
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