Two-dimensional Self-affine Sets with Interior Points , and the Set of Uniqueness

  title={Two-dimensional Self-affine Sets with Interior Points , and the Set of Uniqueness},
  author={Kevin G. Hare},
Let M be a 2 × 2 real matrix with both eigenvalues less than 1 in modulus. Consider two self-affine contraction maps from R → R, Tm(v) = Mv − u and Tp(v) = Mv + u, where u ̸= 0. We are interested in the properties of the attractor of the iterated function system (IFS) generated by Tm and Tp, i.e., the unique non-empty compact set A such that A = Tm(A)∪Tp(A). Our two main results are as follows: • If both eigenvalues of M are between 2−1/4 ≈ 0.8409 and 1 in absolute value, and the IFS is non… CONTINUE READING


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