transition function

Short definition from Wiktionary

Noun

1. 1
   A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state.
2. 2
   A homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,φ₁) and (U_2,φ₂) coordinate charts with U_1∩U_2≠∅, the transition functions φ₁₂=φ₂∘φ₁⁻¹ and its inverse φ₂₁=φ₁∘φ₂⁻¹ may be constructed.