Forme normale d’Arnold et réduction formelle des systèmes d’équations linéaires aux différences

  title={Forme normale d’Arnold et r{\'e}duction formelle des syst{\`e}mes d’{\'e}quations lin{\'e}aires aux diff{\'e}rences},
  author={G. Chen},
  journal={aequationes mathematicae},
  • G. Chen
  • Published 1997
  • Mathematics
  • aequationes mathematicae
SummaryWe study Turrittin’s formal reduction of systems of linear difference equations of the forms $$Y(x + 1) = x^c A(x)Y(x) or Y(x + 1) - Y(x) = x^{ - r/s} A(x)Y(x)$$ . Herec is a rational number;r ands are two positive integers; andA(x)=A0+A1x−1/s+...∈ gl(n, C[[x−1/s]]) withA0≠0; in particular, detA(x)≠0 in the first system. For the reduction in the nilpotent case we use Arnold’s normal form of matrices depending on parameters. We present an algorithm to construct such a normal form for… Expand
5 Citations
Formal reduction of linear difference systems
  • 6
  • PDF
On the stability of canonical forms of singular linear difference systems
  • PDF
Filtration-preserving mappings and centralizers within graded Lie algebras
  • M. Bendersky, Guoting Chen, R. Churchill
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2009
  • PDF