Periodicity of a discrete standard map on 3-dimensional Lattice

Mohamad Hanif, Saleh and Wan Rozali, Wan Nur Fairuz Alwani (2024) Periodicity of a discrete standard map on 3-dimensional Lattice. Journal of Sustainability Science and Management, 19 (8). pp. 39-48. ISSN 1823-8556 E-ISSN 2672-7226

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Abstract

Abstract: The study of resonances of Hamiltonian systems with a divided phase space is a well-established area of research which attracted the interests of many researchers over the years. One can study such resonances over a discrete space. This paper focuses on the rotational motion of the orbits in the 3-dimensional lattice, ℤ3. We construct discrete maps from 2 dimensional to 3-dimensional. We consider the transformations that give periodicity to the 3-dimensional space. On a specific value of initial conditions and parameters alpha and beta, the orbit of the 3-dimensional map is periodic while the rest are non-periodic. Some observations on the reduction from a 3 dimensional map to a 2-dimensional by using principal component analysis (PCA) are investigated analytically in this paper.

Item Type:	Article (Journal)
Uncontrolled Keywords:	Hamiltonian systems, nonlinear rotations, arithmetic dynamics, rotations in 3 -dimensional space, sustainable periodicity.
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA276 Mathematical Statistics Q Science > QA Mathematics > QA300 Analysis
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr Wan Nur Fairuz Alwani Binti Wan Rozali
Date Deposited:	26 Aug 2024 12:39
Last Modified:	22 Oct 2024 14:56
URI:	http://irep.iium.edu.my/id/eprint/114067

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