Studying discrete dynamical systems trough differential equations

Details Studying discrete dynamical systems trough differential equations Studying discrete dynamical systems trough differential equations

2007-02-05

arxiv.org/abs/math/0702121v2

J. Differential Equations 244 (2008), 630--648

Mathematics

Dynamical Systems

22 pages; 3 Figures

Scientific paper

10.1016/j.jde.2007.10.013

In this paper we consider dynamical systems generated by a diffeomorphism F defined on U an open subset of R^n, and give conditions over F which imply that their dynamics can be understood by studying the flow of an associated differential equation, $\dot x=X(x),$ also defined on U. In particular the case where F has n-1 functionally independent first integrals is considered. In this case X is constructed by imposing that it shares with $F$ the same set of first integrals and that the functional equation $\mu(F(x))=\det((DF(x))\mu(x),$ for x in U has some non-zero solution. Several examples for n=2,3 are presented, most of them coming from several well-known difference equations.

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