First integrals of Hamiltonian systems: The inverse problem

Rehana Naz; Fazal M Mahomed; Azam Chaudhry

doi:10.3934/dcdss.2020121

Article Contents

2020, Volume 13, Issue 10: 2829-2840. Doi: 10.3934/dcdss.2020121

This issue Previous Article On sufficiency issues, first integrals and exact solutions of Uzawa-Lucas model with unskilled labor Next Article Exact solutions of a Black-Scholes model with time-dependent parameters by utilizing potential symmetries

First integrals of Hamiltonian systems: The inverse problem

1.
Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan
2.
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa
3.
Department of Economics, Lahore School of Economics, Lahore 53200, Pakistan

^* Corresponding author: Fazal M Mahomed
^* Corresponding author: Fazal M Mahomed

Received: January 2019

Revised: May 2019

Early access: October 31, 2019

Published online: October 31, 2019

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Abstract

There has, to date, been much focus on when a Hamiltonian operator or symmetry results in a first integral for Hamiltonian systems. Very little emphasis has been given to the inverse problem, viz. which operator arises from a first integral of a Hamiltonian system. In this note, we consider this problem with examples mainly taken from economic growth theory. We also provide an example from classical mechanics.

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Mathematics Subject Classification: 37N40, 76M60, 37K05.

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References

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