We begin by studying various topological properties of invariant sets of hyperbolic toral automorphisms in the linear case. Results related to cardinality, local maximality, entropy, and dimension are presented. Where possible, we extend the results to the case of hyperbolic toral automorphisms in higher dimensions, and further to general Anosov maps.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Simmons, Skyler C., "Topological Properties of Invariant Sets for Anosov Maps with Holes" (2011). Theses and Dissertations. 3101.
Dynamical Systems, Open Systems, Hyperbolic Toral Automorphism, Hausdorff Dimension, Box Dimension, Anosov Map