Proof of the exact overlaps conjecture for systems with algebraic contractions
Ariel Rapaport
Abstract
We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
Topics & Concepts
ConjectureMathematicsIterated functionAlgebraic numberReal algebraic geometryAlgebraic cycleAlgebraic surfacePure mathematicsAlgebra over a fieldCollatz conjectureFunction field of an algebraic varietyDiscrete mathematicsMathematical analysisMathematical Dynamics and FractalsAdvanced Differential Equations and Dynamical SystemsQuantum chaos and dynamical systems