Two-Dimensional Discrete Dynamics of Integral Value Transformations

A notion of dimension preservative map, Integral Value Transformations (IVTs) is defined over [Formula: see text] using the set of [Formula: see text]-adic functions. Thereafter, two-dimensional Integral Value Transformations (IVTs) is systematically analyzed over [Formula: see text] using pair of two variable Boolean functions. The dynamics of IVTs over [Formula: see text] is studied from algebraic perspective. It is seen that the dynamics of the IVTs solely depends on the dynamics (state transition diagram) of the pair of two variable Boolean functions. A set of sixteen Collatz-like IVTs are identified in two dimensions. Also, the dynamical system of IVTs having attractor with one, two, three and four cycles is studied. Additionally, some quantitative information of IVTs in different bases and dimensions is also discussed.