A Deterministic Dynamical System Formulation of the Tower of Hanoi with Constant Auxiliary Complexity

This paper presents a structural reformulation of the Tower of Hanoi as a time-dependent deterministic dynamical system. By modeling the configuration space over Z₃ⁿ and introducing a factor map onto Z₃, we isolate the autonomous orbit of the smallest disk. Combining this with 2-adic valuation and Gray code structure, we derive a deterministic transition function that eliminates recursion and achieves Θ(1) auxiliary space complexity.