Geometry of Self-Similar Sets

This paper examines self-similar sets and some of their properties, including the natural equivalence relation found in bilipschitz equivalence. Both dimension and preservation of paths are determined to be invariant under this equivalence. Also, sophisticated techniques, one involving the use of directed graphs, show the equivalence of two spaces.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2007

Author dc:creator

• Roinestad, Kristine A.

Chair dc:contributor.committeechair

• Haskell, Peter E.

Committee members dc:contributor.committeemember

• Day, Martin V.
• Thomson, James E.

• Self-Similarity
• Cantor Sets
• Bilipschitz Equivalence

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05112007-130841

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32581