transition function

Noun

Meaning

(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.

(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


,

φ

1


)


{\displaystyle (U_{1},\varphi _{1})}

and



(

U

2


,

φ

2


)


{\displaystyle (U_{2},\varphi _{2})}

coordinate charts with




U

1


∩

U

2


≠
∅


{\displaystyle U_{1}\cap U_{2}\neq \emptyset }

, the transition functions




φ

12


=

φ

2


∘

φ

1


−
1




{\displaystyle \varphi _{12}=\varphi _{2}\circ \varphi _{1}^{-1}}

and its inverse




φ

21


=

φ

1


∘

φ

2


−
1




{\displaystyle \varphi _{21}=\varphi _{1}\circ \varphi _{2}^{-1}}

may be constructed.
Synonym: transition map

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