Symmetries and first integrals of ordinary difference equations

@article{Hydon2000SymmetriesAF,
  title={Symmetries and first integrals of ordinary difference equations},
  author={Peter E. Hydon},
  journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
  year={2000},
  volume={456},
  pages={2835 - 2855}
}
  • P. Hydon
  • Published 8 December 2000
  • Mathematics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
This paper describes a new symmetry-based approach to solving a given ordinary difference equation. By studying the local structure of the set of solutions, we derive a systematic method for determining one-parameter Lie groups of symmetries in closed form. Such groups can be used to achieve successive reductions of order. If there are enough symmetries, the difference equation can be completely solved. Several examples are used to illustrate the technique for transitive and intransitive… Expand
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