Nonlinear Dynamics

, Volume 96, Issue 4, pp 2225–2239 | Cite as

The approximate Noether symmetries and approximate first integrals for the approximate Hamiltonian systems

  • R. NazEmail author
  • I. Naeem
Original Paper


We provide the Hamiltonian version of the approximate Noether theorem developed for the perturbed ordinary differential equations (ODEs) (Govinder et al. in Phys Lett 240(3):127–131, 1998) for the approximate Hamiltonian systems. We follow the procedure adopted by Dorodnitsyn and Kozlov (J Eng Math 66(1–3):253–270, 2010) for the Hamiltonian systems of unperturbed ODEs. The approximate Legendre transformation connects the approximate Hamiltonian and approximate Lagrangian. The approximate Noether symmetries determining equation for the approximate Hamiltonian systems is defined explicitly. We provide a formula to establish an approximate first integral associated with an approximate Noether symmetry of the approximate Hamiltonian systems. We analyzed several physical models to elaborate the approach developed here.


Approximate Noether symmetries Classification problem Phase space 


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.


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Authors and Affiliations

  1. 1.Centre for Mathematics and Statistical SciencesLahore School of EconomicsLahorePakistan
  2. 2.Department of Mathematics, School of Science and EngineeringLUMSLahore CanttPakistan

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