{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:29:52Z","timestamp":1760239792880,"version":"build-2065373602"},"reference-count":6,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T00:00:00Z","timestamp":1608854400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the present paper, a role of Hamiltonian systems in mathematical and physical formalisms is considered with the help of skew-symmetric differential forms. In classical mechanics the Hamiltonian system is realized from the Euler\u2013Lagrange equation as the integrability condition of the Euler-Lagrange equation and discloses specific features of Lagrange formalism. In the theory of differential equations, the Hamiltonian systems reveals canonical relations that define the integrability conditions of differential equations. The Hamiltonian systems, as a self-independent equations, are an example of dynamic systems that describe a behavior of dynamical systems in phase space. The connection of the Hamiltonian systems with differential equations and dynamical systems point to the fact that dynamical systems can be generated by differential equations. Under the investigation of Hamiltonian systems, in addition to exterior skew-symmetric differential forms it is suggested to use the skew-symmetric differential forms that are defined on a nonintegrable manifolds and possess a nontraditional mathematical apparatus, such as degenerate transformations and transitions from nonintegrable manifold to integral structures.<\/jats:p>","DOI":"10.3390\/sym13010025","type":"journal-article","created":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T09:30:19Z","timestamp":1608888619000},"page":"25","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Qualitative Investigation of Hamiltonian Systems by Application of Skew-Symmetric Differential Forms"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4726-927X","authenticated-orcid":false,"given":"Ludmila","family":"Petrova","sequence":"first","affiliation":[{"name":"Faculty of Computational Mathematics and Cybernetic, Moscow State University, Moscow 119234, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,25]]},"reference":[{"key":"ref_1","unstructured":"Cartan, E. (1945). Les Systemes Differentials Exterieus ef Leurs Application Geometriques, Exposes de Geometrie."},{"key":"ref_2","unstructured":"Schutz, B.F. (1982). Geometrical Methods of Mathematical Physics, Cambrige University Press."},{"key":"ref_3","unstructured":"Petrova, L.I. (2010). Role of Skew-Symmetric Differential Forms in Mathematics. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Arnold, V.I. (1997). Mathematical Methods of Classical Mechanics, Springer.","DOI":"10.1007\/978-3-642-61237-4_1"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Petrova, L.I. (2012). Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor. J. Math. Res., 4.","DOI":"10.5539\/jmr.v4n3p78"},{"key":"ref_6","first-page":"35","article-title":"Basic Principles of the Field Theory: Connection of the Field-Theory Equations with the Equations of Mathematical Physics","volume":"4","author":"Petrova","year":"2017","journal-title":"Int. J. Adv. Res. Phys. Sci. (IJARPS)"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:46:01Z","timestamp":1760179561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,25]]},"references-count":6,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010025"],"URL":"https:\/\/doi.org\/10.3390\/sym13010025","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,12,25]]}}}