Correspondence between One-Parameter group of Linear Transformations and Linear Differential equations that describe Dynamical Systems

  • Marija Miteva
  • Limonka Lazarova


Mathematical formalization of the notion of determined process leads to the notion of one-parameter group of linear transformations. In this paper we define one-parameter group of diffeomorphisms and see their relationship with vector fields, which connect the one-parameter group of diffeomorphisms with differential equations.


B. Piperevski, E. Asprovska, M. Nikolovska: About one-parameter group of linear transformations. Symposium on Differential equations 2010, Strumica, June 2010.

E. Asprovska, B. Piperevski. About stability of the solution of one class linear autonomous systems. Symposium on Differential equations 2010, Strumica, June 2010.

E. L. Ince (1956): Ordinary Differential Equations. Dover Publications, Inc. New York.

G. Ioss, D. D. Joseph (1980): Elementary Stability and Bifurcation Theory. Springer-Verlag, New York, Heidelberg, Berlin.

G. F. Torres del Castillo (2012): Differentiable Manifolds. Springer Science+Business Media, LLC

M. Brin, G. Stuck (2002): Introduction to Dynamical Systems. Cambridge, University Press.

M. Nikolovska (2011): Models of Lorenz and its applications. MSc thesis, Faculty of Electrical Engineering and Information Technologies, Skopje.

S. Smale (1963): Stable manifolds for differential equations and diffeomorphisms. Annali della Scuola Normale Superiore di Pissa, Classe di Scienze, 3e serie, Tome 17, No 1-2 pp.97-116

S. Sastry (1999): Nonlinear Systems, Analysis, Stability and Control. Springer

V. I. Arnold (1978): Ordinary Differential Equations. MIT