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Definitions of transition function:
  • noun:   (computing theory) A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state.
  • noun:   (differential geometry) A homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,๐œ‘โ‚) and (U_2,๐œ‘โ‚‚) coordinate charts with U_1โˆฉU_2โ‰ โˆ…, the transition functions ๐œ‘โ‚โ‚‚=๐œ‘โ‚‚โˆ˜๐œ‘โ‚โปยน and its inverse ๐œ‘โ‚‚โ‚=๐œ‘โ‚โˆ˜๐œ‘โ‚‚โปยน may be constructed.

(Definitions from Wiktionary)

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