Conditions for local reversibility

The paper follows from work by Quispel and Capel on “local reversibility” of a dynamical system. The approach adopted is to write down conditions for a mapping to behave like an involution in the neighbourhood of a fixed point and then to combine mappings which satisfy these conditions, thus producing a composite mapping which is locally reversible. In the main, this confirms the results obtained by Quispel and Capel although additional conditions were found in some cases.