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Abstract: For 0&lambda defined by the three maps fi=λI + pi in the plane, where p0=(0,0), p1=(1-λ,0), p2=(1-λ)(½,1). For &lambda=½ the attractor is the Sierpinski triangle. For λ in the intervals [.6439,.6441], [.6458,.6466], and [.6470,.6472] standard techniques for determining the Hausdorff dimension (or Lebesgue measure) of the "fat" Sierpinski triangle do not apply, a... read morend the Hausdorff dimension has not been known for any specific such λ. For all these λ we show that the attractor has nonempty interior and hence positive Lebesgue measure and Hausdorff dimension 2. The novelty of our approach is that instead of extending techniques developed for small λ we significantly extend geometric methods developed by Broomhead, Montaldi and Sidorov for larger values of λ.
Thesis (Ph.D.)--Tufts University, 2012.
Submitted to the Dept. of Mathematics.
Advisor: Boris Hasselblatt.
Committee: Zbigniew Nitecki, Fulton Gonzalez, and Robert Devaney.
Keyword: Mathematics.read less
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