Algebraic criteria for Lipschitz equivalence of dust‐like self‐similar sets
Lifeng Xi, Ying Xiong
Abstract
This paper concerns the Lipschitz equivalence of dust-like self-similar sets with commensurable ratios. We obtain an algebraic criterion of Falconer–Marsh type to check whether such two self-similar sets are Lipschitz equivalent, and prove that it is a sufficient and necessary condition.
Topics & Concepts
Lipschitz continuityEquivalence (formal languages)MathematicsAlgebraic numberPure mathematicsMathematical analysisMathematical Dynamics and FractalsAdvanced Topology and Set TheoryFunctional Equations Stability Results