Journal of Nonlinear Mathematical Physics

Volume 18, Issue Supplement 1, March 2013, Pages 1 - 31

An Invertible Transformation and Some of its Applications

Authors
M. Bruschi*, , §, F. Calogero*, , , F. Leyvraz, , M. Sommacal*, , **
*Dipartimento di Fisica, Università di Roma “La Sapienza”, 00185, Roma, Italy
Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Italy
Instituto de Ciencias Físicas, UNAM, Cuernavaca, Mexico
Corresponding Author
M. Bruschi
Received 27 September 2010, Accepted 5 October 2010, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925111001258How to use a DOI?
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
Abstract

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.

Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - Supplement 1
Pages
1 - 31
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925111001258How to use a DOI?
Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - M. Bruschi
AU  - F. Calogero
AU  - F. Leyvraz
AU  - M. Sommacal
PY  - 2021
DA  - 2021/01
TI  - An Invertible Transformation and Some of its Applications
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 31
VL  - 18
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001258
DO  - https://doi.org/10.1142/S1402925111001258
ID  - Bruschi2021
ER  -