Two-dimensional Lagrangian singularities and bifurcations of gradient lines I

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dc.creatorMarelli, G.
dc.date2007-03-30
dc.date.accessioned2026-07-07T07:55:06Z
dc.date.available2026-07-07T07:55:06Z
dc.descriptionMotivated by mirror symmetry, we consider a Lagrangian fibration $X\to B$ and Lagrangian maps $f:L\hookrightarrow X\to B$, when $L$ has dimension 2, exhibiting an unstable singularity, and study how their caustic changes, in a neighbourhood of the unstable singularity, when slightly perturbed. The integral curves of $\nabla f_x$, for $x\in B$, where $f_x(y)=f(y)-x\cdot y$, called ``gradient lines'', are then introduced, and a study of them, in order to analyse their bifurcation locus, is carried out.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0703915
dc.identifierhttp://arxiv.org/abs/math/0703915
dc.identifierJ. Geo. Phys. 56/9 (2006), 1688-1708
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126854
dc.subjectDynamical Systems
dc.subjectSymplectic Geometry
dc.subject37G25, 53D12, 70K60
dc.titleTwo-dimensional Lagrangian singularities and bifurcations of gradient lines I
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