2015/12/01 by Andrey Tetenov, Tetenov, Andrey, Kirill Kamalutdinov +3
Mathematics · #28A80 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:28A80
paper · pdf · doi:10.48550/arxiv.1512.00290
23 pages, 6 figures, 2 tables
arxiv created 2016/01/15 · arxiv updated 2016/01/18
It was proved in 2007 by C.Bandt and H.Rao that if a system S = \S1 , ..., Sm \ of contraction similarities in R2 with a connected attractor K has the finite intersection property, then it satisfies OSC. We construct a self-simiilar Jordan arc in R3, defined by a system S , which does not satisfy OSC and at the same time has one-point intersection property.