An invertible transformation and some of its applications

Bruschi, Mario, Calogero, Francesco, Leyvraz, François and Sommacal, Matteo (2011) An invertible transformation and some of its applications. Journal of Nonlinear Mathematical Physics, 18 (s1). pp. 1-31. ISSN 1402-9251

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Several applications of an explicitly invertible transformation are reported. This transformation is elementary and therefore all the results obtained via it might be considered trivial; yet the findings highlighted in this paper are generally far from appearing trivial until the way they are obtained is revealed. Various contexts are considered: algebraic and Diophantine equations, nonlinear Sturm–Liouville problems, dynamical systems (with continuous and with discrete time), nonlinear partial differential equations, analytical geometry, functional equations. While this transformation, in one or another context, is certainly known to many, it does not seem to be as universally known as it deserves to be, for instance it is not routinely taught in basic University courses (to the best of our knowledge). The main purpose of this paper is to bring about a change in this respect; but we also hope that some of the findings reported herein — and the multitude of analogous findings easily obtainable via this technique — will be considered remarkable by the relevant experts, in spite of their elementary origin.

Item Type: Article
Uncontrolled Keywords: invertible transformations, isochronous systems, solvable algebraic and Diophantine equations, solvable nonlinear Sturm–Liouville problems, solvable dynamical systems, solvable Hamiltonian systems, solvable discrete-time dynamical systems, solvable functional equations
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Ellen Cole
Date Deposited: 09 May 2012 11:30
Last Modified: 13 Oct 2019 00:31

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