{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:42:56Z","timestamp":1740120176650,"version":"3.37.3"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,10]]},"abstract":"<jats:p> Connected branches of periodic orbits originating at a Hopf bifurcation point of a differential system are considered. A computable estimate for the range of amplitudes of periodic orbits contained in the branch is provided under the assumption that the nonlinear terms satisfy a linear estimate in a ball. If the estimate is global, then the branch is unbounded. The results are formulated in an equivariant setting where the system can have multiple branches of periodic orbits characterized by different groups of symmetries. The nonlocal analysis is based on the equivariant degree method, which allows us to handle both generic and degenerate Hopf bifurcations. This is illustrated by examples. <\/jats:p>","DOI":"10.1142\/s0218127420501989","type":"journal-article","created":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T01:22:12Z","timestamp":1604020932000},"page":"2050198","source":"Crossref","is-referenced-by-count":0,"title":["Guaranteed Estimates for the Length of Branches of Periodic Orbits for Equivariant Hopf Bifurcation"],"prefix":"10.1142","volume":"30","author":[{"given":"Edward","family":"Hooton","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Czech Academy of Sciences, \u017ditn\u00e1 25, 11567, Prague 11567, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3218-7290","authenticated-orcid":false,"given":"Zalman","family":"Balanov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, The University of Texas at Dallas, 800 West Campbell Road, Richardson, TX 75080, USA"},{"name":"Department of Mathematics, Xiangnan University, 889 Chen Zhou Da Dao, Chenzhou, Hunan 423000, P. 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