Arithmetic Dynamical Spaces for Residue-Affine and Accelerated q x + ρ qx+ρ Maps: Congruence Algebra, Valuation Branches, and Inherited Density

AbstractWe define an arithmetic dynamical space that encodes the evolution of integer sequences under generalized Qx+RQx+R maps and study its measure-theoretic and graph-topological properties. Keywordsresidue-affine maps; arithmetic dynamical space; inherited density; congruence dynamics; valuation histories; path measure; generalized accelerated Collatz maps