Semi-conjugacies to tent maps, transitivity and patterns, and inverse limit spaces
by Ledis, Dennis Joel, Ph.D., UNIVERSITY OF FLORIDA, 2011, 49 pages; 3497061

Abstract:

Let f be a continuous map of the interval to itself. We prove that if f has a k-horseshoe, then f is topologically semi-conjugate to a tent map with slope ± k. Moreover, we prove that if f is topologically transitive, exhibits a particular pattern as a piecewise linear map L, and h(f) = h( L), then f is topologically conjugate to L. Using the first result, we prove that if f has positive topological entropy, and n ≥ 2, then there is a continuous surjective map from the inverse limit space (I, f) to the Knaster continuum Kn. In particular, for m, n ≥ 2, there is a continuous surjective map from Km to Kn. On the other hand, we prove that the analogous statement does not hold for solenoids.

 
AdviserLouis Block
SchoolUNIVERSITY OF FLORIDA
SourceDAI/B 73-06, p. , Feb 2012
Source TypeDissertation
SubjectsMathematics; Theoretical mathematics
Publication Number3497061
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