{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T05:11:54Z","timestamp":1775020314182,"version":"3.50.1"},"reference-count":17,"publisher":"Pleiades Publishing Ltd","issue":"8","license":[{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Program Comput Soft"],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1134\/s0361768823080030","type":"journal-article","created":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T09:30:41Z","timestamp":1706088641000},"page":"842-853","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Symbolic Computation of an Arbitrary-Order Resonance Condition in a Hamiltonian System"],"prefix":"10.1134","volume":"49","author":[{"given":"A. B.","family":"Batkhin","sequence":"first","affiliation":[]},{"given":"Z. Kh.","family":"Khaidarov","sequence":"additional","affiliation":[]}],"member":"137","published-online":{"date-parts":[[2024,1,24]]},"reference":[{"key":"3791_CR1","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1002\/cpa.3160110105","volume":"11","author":"J.K. Moser","year":"1958","unstructured":"Moser, J.K., New aspects in the theory of stability of Hamiltonian systems, Commun. Pure Appl. Math., 1958, vol. 11, no. 1, pp. 81\u2013114.","journal-title":"Commun. Pure Appl. Math."},{"key":"3791_CR2","doi-asserted-by":"publisher","unstructured":"Batkhin, A.B. and Khaidarov, Z.Kh., Strong resonances in a nonlinear Hamiltonian system, Preprint of Keldysh Inst. Appl. Math, Russ. Acad. Sci., 2022, no. 59, pp. 1\u201328. https:\/\/doi.org\/10.20948\/prepr-2022-59","DOI":"10.20948\/prepr-2022-59"},{"key":"3791_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-87284-6","volume-title":"Lectures on Celestial Mechanics","author":"C.L. Siegel","year":"1971","unstructured":"Siegel, C.L. and Moser, J.K., Lectures on Celestial Mechanics, Springer, 1971."},{"key":"3791_CR4","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.jappmathmech.2012.03.006","volume":"76","author":"A.B. Batkhin","year":"2012","unstructured":"Batkhin, A.B., Bryuno, A.D., and Varin, V.P., Stability sets for multiparameter Hamiltonian systems, J. Appl. Math. Mech., 2012, vol. 76, no. 1, pp. 80\u2013133. https:\/\/doi.org\/10.1016\/j.jappmathmech.2012.03.006","journal-title":"J. Appl. Math. Mech."},{"key":"3791_CR5","unstructured":"Kalinina, E.A. and Uteshev, A.Yu., Teoriya isk-lyucheniya:\u00a0Uchebnoe posobie (Elimination Theory: A Study Guide), St. Petersburg: Izd. Nauchn. Issled. Inst. Khim. S.-Peterb. Gos. Univ., 2002."},{"key":"3791_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-33099-2","volume-title":"Algorithms in Real Algebraic Geometry","author":"S. Basu","year":"2006","unstructured":"Basu, S., Pollack, R., and Roy, M.-F., Algorithms in Real Algebraic Geometry, Springer, 2006."},{"key":"3791_CR7","first-page":"199","volume":"26","author":"A.D. Bryuno","year":"1972","unstructured":"Bryuno, A.D., Analytical form of differential equations (II), Tr. Mosk. Mat, O-va., 1972, vol. 26, pp. 199\u2013239.","journal-title":"O-va."},{"key":"3791_CR8","doi-asserted-by":"crossref","unstructured":"Bryuno, A.D., Restricted Three-Body Problem: Plane Periodic Orbits, de Gruyter, New York, 1994.","DOI":"10.1515\/9783110901733"},{"key":"3791_CR9","doi-asserted-by":"crossref","unstructured":"Birkhoff, G.D., Dynamical Systems, Am. Math. Soc., 1927.","DOI":"10.1090\/coll\/009"},{"key":"3791_CR10","doi-asserted-by":"crossref","unstructured":"Bruno, A.D. and Batkhin, A.B., Survey of eight modern methods of Hamiltonian mechanics, Axioms, 2021, vol. 10, no. 4. \nhttps:\/\/www.mdpi.com\/2075-1680\/10\/4\/293","DOI":"10.3390\/axioms10040293"},{"key":"3791_CR11","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1007\/BF01098887","volume":"1","author":"A.D. Bryuno","year":"1967","unstructured":"Bryuno, A.D., On the formal stability of Hamiltonian systems, Mat. Notes, 1967, vol. 1, no. 3, pp. 216\u2013219.","journal-title":"Mat. Notes"},{"key":"3791_CR12","unstructured":"Zhuravlev, V.F., Petrov, A.G., and Shunderyuk, M.M., Izbrannye zadachi gamil\u2019tonovoi mekhaniki (Selected Problems of Hamiltonian Mechanics), Moscow: LENAND, 2015."},{"key":"3791_CR13","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1134\/S0361768818020032","volume":"63","author":"A.B. Batkhin","year":"2023","unstructured":"Batkhin, A.B. and Khaidarov, Z.Kh., Calculation of a strong resonance condition in a Hamiltonian system, Comput. Math. Math. Phys., 2023, vol. 63, pp. 687\u2013703. https:\/\/doi.org\/10.1134\/S0361768818020032","journal-title":"Comput. Math. Math. Phys."},{"key":"3791_CR14","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1134\/S0361768823010036","volume":"49","author":"A.D. Bruno","year":"2023","unstructured":"Bruno, A.D. and Azimov, A.A., Computing unimodular matrices of power transformations, Program. Comput. Softw., 2023, vol. 49, no. 1, pp. 32\u201341. https:\/\/doi.org\/10.1134\/S0361768823010036","journal-title":"Program. Comput. Softw."},{"key":"3791_CR15","doi-asserted-by":"publisher","first-page":"5","DOI":"10.15688\/jvolsu1.2016.4.1","volume":"35","author":"A.B. Batkhin","year":"2016","unstructured":"Batkhin, A.B., Resonant set of a polynomial and the formal stability problem, Vestn. Volgogr. Gos. Univ., Ser.\u00a01 Mat, Fiz., 2016, vol. 35, no. 4, pp. 5\u201323. (in Russian). https:\/\/doi.org\/10.15688\/jvolsu1.2016.4.1","journal-title":"Fiz."},{"key":"3791_CR16","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1134\/S0361768818020032","volume":"44","author":"A.B. Batkhin","year":"2018","unstructured":"Batkhin, A.B., Parameterization of a set determined by the generalized discriminant of a polynomial, Program. Comput. Softw., 2018, vol. 44, pp. 75\u201385. https:\/\/doi.org\/10.1134\/S0361768818020032","journal-title":"Program. Comput. Softw."},{"key":"3791_CR17","doi-asserted-by":"publisher","first-page":"27","DOI":"10.20537\/nd1301003","volume":"9","author":"A.P. Markeev","year":"2013","unstructured":"Markeev, A.P., A motion of connected pendulums, Russ. J. Nonlin. Dyn., 2013, vol. 9, no. 1, pp. 27\u201338. https:\/\/doi.org\/10.20537\/nd1301003","journal-title":"Russ. J. Nonlin. Dyn."}],"container-title":["Programming and Computer Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768823080030.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0361768823080030","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768823080030.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T03:14:32Z","timestamp":1775013272000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0361768823080030"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12]]},"references-count":17,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["3791"],"URL":"https:\/\/doi.org\/10.1134\/s0361768823080030","relation":{},"ISSN":["0361-7688","1608-3261"],"issn-type":[{"value":"0361-7688","type":"print"},{"value":"1608-3261","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12]]},"assertion":[{"value":"10 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 December 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 February 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 January 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflicts of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"CONFLICT OF INTEREST"}}]}}