Browsing by Author "Bruin, H."
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- ItemFibonacci-like unimodal inverse limit spaces(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Bruin, H.; Štimac, S.We study the structure of inverse limit space of so-called Fibonacci-like tent maps. The combinatorial constraints implied by the Fibonacci-like assumption allows us to introduce certain chains that enable a more detailed analysis of symmetric arcs within this space than is possible in the general case. We show that link-symmetric arcs are always symmetric or a well-understood concatenation of quasi-symmetric arcs. This leads to simplification of some existing results, including the Ingram Conjecture for Fibonacci-like unimodal inverse limits.
- ItemThe Ingram Conjecture(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Barge, M.; Bruin, H.; Stimac, S.We prove the Ingram Conjecture, i.e., we show that the inverse limit spaces of ev- ery two tent maps with di®erent slopes in the interval [1; 2] are non-homeomorphic. Based on the structure obtained from the proof, we also show that every self- homeomorphism of the inverse limit space of the tent map is pseudo-isotopic, on the core, to some power of the shift homeomorphism.