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Math."],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>In this paper we introduce the concept of rotation cones, determined by rotation sets, and use these to describe the stability of rotation sets of incompressible and fixed-point free continuous flows on the torus <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathbb{T}^{d}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>T<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mrow>\n                      <mml:mi>d<\/mml:mi>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>, <jats:italic>d<\/jats:italic> \u2a7e 2. The previous concept is equivalent and extends the stability of rotation numbers (and rotation vectors) in the special case of fixed-point free continuous flows on <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathbb{T}^{2}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>T<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mrow>\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. We prove that incompressible Lipschitz vector fields with stable rotation sets have convex rotation cones with non-empty interior, and that all extremal edges are collinear with vectors in \u2124<jats:sup>\n              <jats:italic>d<\/jats:italic>\n            <\/jats:sup>. If, in addition, the rotation cones are proper, then these are polyhedral with finitely many edges. Finally we prove that the set of vector fields with stable rotation sets is <jats:italic>C<\/jats:italic>\n            <jats:sup>0<\/jats:sup>-open and dense among those having proper rotation cones.<\/jats:p>","DOI":"10.1007\/s11856-024-2672-3","type":"journal-article","created":{"date-parts":[[2024,10,31]],"date-time":"2024-10-31T08:24:45Z","timestamp":1730363085000},"page":"729-768","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Shape and stability of rotation sets for incompressible flows on the torus"],"prefix":"10.1007","volume":"265","author":[{"given":"Wescley","family":"Bonomo","sequence":"first","affiliation":[]},{"given":"Heides","family":"Lima","sequence":"additional","affiliation":[]},{"given":"Paulo","family":"Varandas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,10,28]]},"reference":[{"key":"2672_CR1","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1017\/S0143385703000336","volume":"24","author":"S Addas-Zanata","year":"2004","unstructured":"S. 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