# Factorizable Lie symmetries and the linearization of difference equations

@inproceedings{Byrnes1995FactorizableLS, title={Factorizable Lie symmetries and the linearization of difference equations}, author={Graham B. Byrnes and Ramajayam Sahadevan and Gilles. Quispel}, year={1995} }

- Published 1995
DOI:10.1088/0951-7715/8/3/009

We show that an autonomous difference equation, of arbitrary order and with one or more independent variables, can be linearized by a point transformation if and only if it admits a symmetry vector field whose coefficient function is the product of two functions, one of the dependent variable u and one of the independent variables x: X(x, u)=A(x)G(u) partial/partial u . The factor depending on the independent variables, A, is required to satisfy some non-degeneracy conditions. This result is… CONTINUE READING

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## Continuous symmetries of difference equations.

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