Agafonov, Serguei [UNESP]2015-04-272015-04-272014Geometriae Dedicata, v. 176, n. 1, p. 87-115, 2014.1572-9168http://hdl.handle.net/11449/122674Implicit ODE, cubic in derivative, generically has no infinitesimal symmetries even at regular points with distinct roots. Cartan showed that at regular points, ODEs with hexagonal 3-web of solutions have symmetry algebras of the maximal possible dimension 3. At singular points such a web can lose all its symmetries. In this paper we study hexagonal 3-webs having at least one infinitesimal symmetry at singular points. In particular, we establish sufficient conditions for the existence of non-trivial symmetries and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling in some coordinates. Using the obtained results, we provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection form is holomorphic at the singular point, 2) the web admits at least one infinitesimal symmetry at this point. As a by-product, a classification of hexagonal weighted homogeneous 3-webs is obtained.1-29engHexagonal 3-webInfinitesimal symmetriesChern connectionImplicit ODEArtigo10.1007/s10711-014-9960-8Acesso restrito8731229576624291