6533b7d1fe1ef96bd125d805

RESEARCH PRODUCT

IFS attractors and Cantor sets

Michał RamsSylvain Crovisier

subject

Cantor's theoremDiscrete mathematicsMathematics::Dynamical SystemsAntoine's necklaceCantor set[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]010102 general mathematicsMathematics::General TopologyCantor function01 natural sciences010101 applied mathematicsCombinatoricsNull setCantor setsymbols.namesakeMetric spaceAttractorsymbolsGeometry and Topology0101 mathematicsAntoine's necklaceCantor's diagonal argumentIterated function systemMathematics

description

Abstract We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R 3 such that every homeomorphism f of R 3 which preserves K coincides with the identity on K.

yearjournalcountryeditionlanguage
2006-05-01Topology and its Applications
https://doi.org/10.1016/j.topol.2005.06.010