Eur. Phys. J. Special Topics 165, 61-71 (2008)
https://doi.org/10.1140/epjst/e2008-00849-9

Dynamical systems generated by two alternating vector fields

Department of Mathematics, Prague Institute of Chemical Technology, Technicka 5, 16628 Prague, Czech Republic

Corresponding author: Pavel.Pokorny@vscht.cz

Abstract

Dynamical systems generated by two vector fields that alternate in time are investigated. The flow of each vector field is expressed as the exponential of a differential operator and the composition of the two flows can then be found as the composition of the two exponentials. A single autonomous vector field is found with the same period map. This vector field is shown to be expressed by the Baker-Campbell-Hausdorff formula.