caa a22 4500 386382972 CHVBK 20180307112049.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500025087 doi S0308210500025087 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500025087 On binary differential equations and umbilics [Elektronische Daten] In this paper we give the local classification of solution curves of bivalued direction fields determined by the equation where a and b are smooth functions which we suppose vanish at 0 ∈ ℝ2. Such fields arise on surfaces in Euclidean space, near umbilics, as the principal direction fields, and also in applications of singularity theory to the structure of flow fields and monochromatic-electromagnetic radiation. We give a classification up to homeomorphism (there are three types) but the methods furnish much additional information concerning the fields, via a crucial blowing-up construction. Copyright © Royal Society of Edinburgh 1989 Bruce J.W. Department of Mathematics, University of Newcastle upon Tyne, Newcastle NE1 7RU, U.K. Fidal D.L. Department of Mathematics, University of Newcastle upon Tyne, Newcastle NE1 7RU, U.K. Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/1-2(1989), 147-168 0308-2105 111:1-2<147 1989 111 PRM https://doi.org/10.1017/S0308210500025087 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500025087 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bruce J.W. Department of Mathematics, University of Newcastle upon Tyne, Newcastle NE1 7RU, U.K NATIONALLICENCE 700 1- Fidal D.L. Department of Mathematics, University of Newcastle upon Tyne, Newcastle NE1 7RU, U.K NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/1-2(1989), 147-168 0308-2105 111:1-2<147 1989 111 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge