@article {Błaszak:2012:0022-2526:26,
title = "On Reciprocal Equivalence of St{\"a}ckel Systems",
journal = "Studies in Applied Mathematics",
parent_itemid = "infobike://bpl/sapm",
publishercode ="bp",
year = "2012",
volume = "129",
number = "1",
publication date ="2012-07-01T00:00:00",
pages = "26-50",
itemtype = "ARTICLE",
issn = "0022-2526",
eissn = "1467-9590",
url = "https://www.ingentaconnect.com/content/bpl/sapm/2012/00000129/00000001/art00002",
doi = "doi:10.1111/j.1467-9590.2011.00544.x",
author = "Baszak, By Maciej and Marciniak, Krzysztof",
abstract = "In this paper we investigate St{\"a}ckel transforms between different classes of parameterdependent St{\"a}ckel separable systems of the same dimension. We show that the set of all St{\"a}ckel systems of the same dimension splits to equivalence classes so that all members
within the same class can be connected by a single St{\"a}ckel transform. We also give an explicit formula relating solutions of two St{\"a}ckelrelated systems. These results show in particular that any two geodesic St{\"a}ckel systems are St{\"a}ckel equivalent in the sense that
it is possible to transform one into another by a single St{\"a}ckel transform. We also simplify proofs of some known statements about multiparameter St{\"a}ckel transform.",
}