{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,29]],"date-time":"2025-11-29T08:04:17Z","timestamp":1764403457181,"version":"build-2065373602"},"reference-count":65,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T00:00:00Z","timestamp":1740355200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"VRIDT","award":["096\/2022","098\/2022"],"award-info":[{"award-number":["096\/2022","098\/2022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We explore nonlocal symmetries in a class of Hamiltonian dynamical systems governed by second-order differential equations. Specifically, we establish an algorithm for deriving nonlocal symmetries by utilizing the Jacobi metric and the Eisenhart\u2013Duval lift to geometrize the dynamical systems. The geometrized systems often exhibit additional local symmetries compared to the original systems, some of which correspond to nonlocal symmetries for the original formulation. This novel approach allows us to determine nonlocal symmetries in a systematic way. Within this geometric framework, we demonstrate that the second-order differential equation q\u00a8\u2212Fq=0 admits an infinite number of nonlocal symmetries generated by the infinite-dimensional conformal algebra of a two-dimensional Riemannian manifold. Applications to higher-dimensional systems are also discussed.<\/jats:p>","DOI":"10.3390\/sym17030340","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T07:46:57Z","timestamp":1740383217000},"page":"340","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Novel Method to Calculate Nonlocal Symmetries from Local Symmetries"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9966-5517","authenticated-orcid":false,"given":"Andronikos","family":"Paliathanasis","sequence":"first","affiliation":[{"name":"Institute of Systems Science, Faculty of Applied Sciences, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa"},{"name":"Departamento de Matem\u00e1ticas, Universidad Cat\u00f3lica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta 1270709, Chile"},{"name":"Centre for Space Research, North-West University, Potchefstroom 2520, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"012001","DOI":"10.1088\/1742-6596\/722\/1\/012001","article-title":"Conservation laws and symmetries of the shallow water system above rough bottom","volume":"722","author":"Aksenov","year":"2016","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.camwa.2015.10.016","article-title":"Application of Lie groups to compressible model of two-phase flows","volume":"71","author":"Bira","year":"2016","journal-title":"Comput. Math. 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