{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T17:01:24Z","timestamp":1761930084947,"version":"3.37.3"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p> We examine the convergence properties of the generalized H\u00e9non\u2013Heiles system, by using the multivariate version of the Newton\u2013Raphson iterative scheme. In particular, we numerically investigate how the perturbation parameter [Formula: see text] influences several aspects of the method, such as its speed and efficiency. Color-coded diagrams are used for revealing the basins of convergence on the configuration plane. Additionally, we compute the degree of fractality of the convergence basins on the configuration space, as a function of the perturbation parameter, by using different tools, such the uncertainty dimension and the (boundary) basin entropy. Our analysis suggests that the perturbation parameter strongly influences the number of the equilibrium points, as well as the geometry and the structure of the associated basins of convergence. Furthermore, the highest degree of fractality, along with the appearance of nonconverging points, occur near the critical values of the perturbation parameter. <\/jats:p>","DOI":"10.1142\/s0218127420500078","type":"journal-article","created":{"date-parts":[[2020,2,14]],"date-time":"2020-02-14T01:35:40Z","timestamp":1581644140000},"page":"2050007","source":"Crossref","is-referenced-by-count":3,"title":["Determining the Properties of the Basins of Convergence in the Generalized H\u00e9non\u2013Heiles System"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1565-4467","authenticated-orcid":false,"given":"Euaggelos E.","family":"Zotos","sequence":"first","affiliation":[{"name":"Department of Physics, School of Science, Aristotle University of Thessaloniki, GR-541 24, Thessaloniki, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Md.","family":"Sanam Suraj","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Aurobindo College, University of Delhi, New Delhi-110017, Delhi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amit","family":"Mittal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, ARSD College, University of Delhi, New Delhi-110021, Delhi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rajiv","family":"Aggarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Deshbandhu College, University of Delhi, New Delhi-110019, Delhi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,2,12]]},"reference":[{"key":"S0218127420500078BIB001","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.64.066208"},{"key":"S0218127420500078BIB002","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.81.333"},{"key":"S0218127420500078BIB003","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.042214"},{"key":"S0218127420500078BIB004","doi-asserted-by":"publisher","DOI":"10.1038\/srep31416"},{"key":"S0218127420500078BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-68109-2_2"},{"key":"S0218127420500078BIB006","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/215.4.731"},{"key":"S0218127420500078BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2018.02.001"},{"key":"S0218127420500078BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(83)90945-3"},{"key":"S0218127420500078BIB009","doi-asserted-by":"publisher","DOI":"10.1086\/109234"},{"key":"S0218127420500078BIB010","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.65.015205"},{"key":"S0218127420500078BIB011","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.69.066218"},{"key":"S0218127420500078BIB012","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.71.026227"},{"volume-title":"Chaos in Dynamical Systems","year":"1993","author":"Ott E.","key":"S0218127420500078BIB013"},{"key":"S0218127420500078BIB014","volume-title":"Numerical Recipes in FORTRAN 77","author":"Press H. 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