{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:52:13Z","timestamp":1762955533930,"version":"3.45.0"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Publ. Res. Inst. Math. Sci."],"published-print":{"date-parts":[[1988,6,30]]},"abstract":"<jats:p>\n                    Let\n                    <jats:inline-formula>\n                      <jats:tex-math>X<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    be a complex analytic manifold and let\n                    <jats:inline-formula>\n                      <jats:tex-math>Y<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    be a submanifold of\n                    <jats:inline-formula>\n                      <jats:tex-math>X<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . We introduce\nthe notion of \u201cfuchsian differential System along\n                    <jats:inline-formula>\n                      <jats:tex-math>Y<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    \u201d, and we prove that for such Systems\nthe meromorphic solutions and those with essential singularities are the same. We prove as\nwell that the formal solutions (along\n                    <jats:inline-formula>\n                      <jats:tex-math>Y<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ) always converge. These results are well-known\nin the regular holonomic case.\n                  <\/jats:p>\n                  <jats:sec>\n                    <jats:title>R\u00e9sum\u00e9<\/jats:title>\n                    <jats:p>\n                      Soit\n                      <jats:inline-formula>\n                        <jats:tex-math>X<\/jats:tex-math>\n                      <\/jats:inline-formula>\n                      une vari\u00e9t\u00e9 analytique complexe et\n                      <jats:inline-formula>\n                        <jats:tex-math>Y<\/jats:tex-math>\n                      <\/jats:inline-formula>\n                      une sous-vari\u00e9t\u00e9 lisse de\n                      <jats:inline-formula>\n                        <jats:tex-math>X<\/jats:tex-math>\n                      <\/jats:inline-formula>\n                      . Nous introduisons la notion de \u201csyst\u00e8me diff\u00e9rentiel fuchsien le long de\n                      <jats:inline-formula>\n                        <jats:tex-math>Y<\/jats:tex-math>\n                      <\/jats:inline-formula>\n                      \u201d, et nous montrons que pour de tels syst\u00e8mes les solutions m\u00e9romorphes et les solutions \u00e0 singularit\u00e9s essentielles sont les m\u00eames. Nous montrons aussi que les solutions formelles (le long de\n                      <jats:inline-formula>\n                        <jats:tex-math>Y<\/jats:tex-math>\n                      <\/jats:inline-formula>\n                      ) sont toujours convergentes. Ces r\u00e9sultats sont bien connus dans le cas holon\u00f4me singulier r\u00e9gulier.\n                    <\/jats:p>\n                  <\/jats:sec>","DOI":"10.2977\/prims\/1195175034","type":"journal-article","created":{"date-parts":[[2008,1,24]],"date-time":"2008-01-24T12:03:32Z","timestamp":1201176212000},"page":"397-431","source":"Crossref","is-referenced-by-count":8,"title":["Syst\u00e8mes Diff\u00e9rentiels Fuchsiens le Long d'une Sous-Vari\u00e9t\u00e9"],"prefix":"10.4171","volume":"24","author":[{"given":"Yves","family":"Laurent","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris-Sud, Orsay, France"}]},{"given":"Teresa","family":"Monteiro Fernandes","sequence":"additional","affiliation":[{"name":"Universidade de Lisboa, Portugal"}]}],"member":"2673","container-title":["Publications of the Research Institute for Mathematical Sciences"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.2977\/prims\/1195175034","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:42:13Z","timestamp":1762954933000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.2977\/prims\/1195175034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,6,30]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2977\/prims\/1195175034","relation":{},"ISSN":["0034-5318","1663-4926"],"issn-type":[{"type":"print","value":"0034-5318"},{"type":"electronic","value":"1663-4926"}],"subject":[],"published":{"date-parts":[[1988,6,30]]}}}