Characterization and solvability of quasipolynomial symplectic mappings

TL;DR

This paper characterizes quasipolynomial symplectic mappings, demonstrating their explicit solutions and broad applicability across fields like physics and economics, thus advancing understanding of their structure and solvability.

Contribution

It provides a complete characterization of quasipolynomial symplectic mappings and shows they all have explicit analytical solutions, expanding the theoretical framework and solution methods.

Findings

All QP symplectic mappings are explicitly solvable.

QP formalism aids in characterizing symplectic mappings.

Examples illustrate the theoretical results.

Abstract

Quasipolynomial (or QP) mappings constitute a wide generalization of the well-known Lotka-Volterra mappings, of importance in different fields such as population dynamics, Physics, Chemistry or Economy. In addition, QP mappings are a natural discrete-time analog of the continuous QP systems, which have been extensively used in different pure and applied domains. After presenting the basic definitions and properties of QP mappings in a previous article \cite{bl1}, the purpose of this work is to focus on their characterization by considering the existence of symplectic QP mappings. In what follows such QP symplectic maps are completely characterized. Moreover, use of the QP formalism can be made in order to demonstrate that all QP symplectic mappings have an analytical solution that is explicitly and generally constructed. Examples are given.