{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T08:16:47Z","timestamp":1774685807406,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"accepted":{"date-parts":[[2025,4,10]]},"published-print":{"date-parts":[[2025,6,13]]},"abstract":"<jats:p>\n                    We consider the characterization of global attractors\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{A}_{f}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    for semiflows generated by scalar one-dimensional semilinear parabolic equations of the form\n                    <jats:inline-formula>\n                      <jats:tex-math>u_{t} = u_{xx}+ f(u,u_{x})<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , defined on the circle\n                    <jats:inline-formula>\n                      <jats:tex-math>x\\in S^{1}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , for a class of reversible nonlinearities. Given two reversible nonlinearities,\n                    <jats:inline-formula>\n                      <jats:tex-math>f_{0}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:tex-math>f_{1}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , with the same lap signature, we prove the existence of a reversible homotopy\u00a0\n                    <jats:inline-formula>\n                      <jats:tex-math>f_{\\tau}, 0\\le\\tau\\le 1<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , which preserves all heteroclinic connections. Consequently, we obtain a classification of the connection graphs of global attractors in the class of reversible nonlinearities. We also describe bifurcation diagrams which reduce a global attractor\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{A}_{1}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    to the trivial global attractor\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{A}_{0}=\\{0\\}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>","DOI":"10.4171\/pm\/2144","type":"journal-article","created":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T09:48:43Z","timestamp":1749808123000},"page":"297-323","source":"Crossref","is-referenced-by-count":3,"title":["Classification of connection graphs of global attractors for $S^{1}$-equivariant parabolic equations"],"prefix":"10.4171","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3994-2834","authenticated-orcid":false,"given":"Carlos","family":"Rocha","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Lisboa, Lisbon, Portugal"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:13:09Z","timestamp":1762261989000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/2144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,13]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.4171\/pm\/2144","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"value":"0032-5155","type":"print"},{"value":"1662-2758","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,13]]}}}