Abstract
Elementary version of moving frame method is applied to the symmetries and equivalences of second-order difference equations. Close links to the web theory and Riemannian geometry are established.
Similar content being viewed by others
References
BLASCHKE, W.: Geometrie der Waben (Sammlung “Elemente der Mathematik vom höheren Standpunkt aus” Bd. 4), Birkhäuser Verlag, Basel-Stuttgart, 1955 (German).
CARTAN, É.: Les problémes d’èquivalence. In: OEuvrès Completes, Partie II, Vol. 2, Gauthier-Villars, Paris, 1953, pp. 1311–1334; Les problémes d’èquivalence Gauthier-Villars, Paris, 1939 (French).
CHRASTINA, J.: The Formal Theory of Differential Equations. Folia Fac. Scient. Nat. Univ. Masarykianae Brunensis, Mathematica 6, Masaryk University, Brno, 1998.
GARDNER, R. B.: The method of equivalence and its applications. SIAM, CBMS-NSF Regional Conference Series in Applied Mathematics 58, SIAM, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1989.
HYDON, P. E.: Symmetries and first integrals of ordinary difference equations, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456 (2000), No. 2004, 2835–2855.
JENSEN, G. R.: Higher order contact of submanifolds of homogeneous spaces. Lecture Notes in Math. 610, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
OLVER, P. J.: Equivalence, Invariants and Symmetry, Cambridge University Press, Cambridge, 1995.
STERNBERG, S.: Lectures on Differential Geometry. Prentice-Hall Mathematics Series, Prentice-Hall, Inc., Englewood Cliffs, 1964.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Michal Fečkan
This research has been conducted at the Department of Mathematics as part of the research project CEZ: Progressive Reliable and Durable Structures, MSM 0021630519.
About this article
Cite this article
Tryhuk, V., Chrastinová, V. Equivalence of difference equations within the web theory. Math. Slovaca 62, 735–750 (2012). https://doi.org/10.2478/s12175-012-0041-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s12175-012-0041-x