We prove that for a given impulsive dynamical system there exists an isomorphism of the basic dynamical system such that in the new system equipped with the same impulse function each impulsive trajectory is global, i.e. the resulting dynamics is defined for all positive times. We also prove that for a given impulsive system it is possible to change the topology in the phase space so that we may consider the system as a semidynamical system (without impulses).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-1,
author = {Krzysztof Ciesielski},
title = {On time reparametrizations and isomorphisms of impulsive dynamical systems},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {1-25},
zbl = {1098.37015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-1}
}
Krzysztof Ciesielski. On time reparametrizations and isomorphisms of impulsive dynamical systems. Annales Polonici Mathematici, Tome 83 (2004) pp. 1-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-1/