{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T02:10:57Z","timestamp":1686017457757},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2011,7]]},"abstract":"<jats:p>We study cubic vector fields with inverse radial symmetry, i.e. of the form \u1e8b = \u03b4x - y + ax<jats:sup>2<\/jats:sup>+ bxy + cy<jats:sup>2<\/jats:sup>+ \u03c3(dx - y)(x<jats:sup>2<\/jats:sup>+ y<jats:sup>2<\/jats:sup>), \u1e8f = x + \u03b4y + ex<jats:sup>2<\/jats:sup>+ fxy + gy<jats:sup>2<\/jats:sup>+ \u03c3(x + dy) (x<jats:sup>2<\/jats:sup>+ y<jats:sup>2<\/jats:sup>), having a center at the origin and at infinity; we shortly call them cubic irs-systems. These systems are known to be Hamiltonian or reversible. Here we provide an improvement of the algorithm that characterizes these systems and we give a new normal form.<\/jats:p><jats:p>Our main result is the systematic classification of the global phase portraits of the cubic Hamiltonian irs-systems respecting time (i.e. \u03c3 = 1) up to topological and diffeomorphic equivalence. In particular, there are 22 (resp. 14) topologically different global phase portraits for the Hamiltonian (resp. reversible Hamiltonian) irs-systems on the Poincar\u00e9 disc.<\/jats:p><jats:p>Finally we illustrate how to generalize our results to polynomial irs-systems of arbitrary degree. In particular, we study the bifurcation diagram of a 1-parameter subfamily of quintic Hamiltonian irs-systems. Moreover, we indicate how to construct a concrete reversible irs-system with a given configuration of singularities respecting their topological type and separatrix connections.<\/jats:p>","DOI":"10.1142\/s0218127411029501","type":"journal-article","created":{"date-parts":[[2011,4,5]],"date-time":"2011-04-05T10:59:24Z","timestamp":1302001164000},"page":"1831-1867","source":"Crossref","is-referenced-by-count":5,"title":["GLOBAL CLASSIFICATION OF A CLASS OF CUBIC VECTOR FIELDS WHOSE CANONICAL REGIONS ARE PERIOD ANNULI"],"prefix":"10.1142","volume":"21","author":[{"given":"M.","family":"CAUBERGH","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"LLIBRE","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"TORREGROSA","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"19","volume":"1954","author":"Bautin N. 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