An Invertible Transformation and Some of its Applications
- 10.1142/S1402925111001258How to use a DOI?
- 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
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.
- © 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 - 2021/01/07 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 - 10.1142/S1402925111001258 ID - Bruschi2021 ER -