Summary
Our main result is as follows. LetNbe a closed manifold and letL ={L t } be an exact, compactly supported family of Lagrangian submanifolds of the symplectic manifoldM=T*(N) such that Lo admits a generating family quadratic at infinity. Letp: [0,1]→Mbe a path of intersection points of LtwithN. Assume thatL t is transversal toNatp(t) fort= 0,1, and that the Maslov interection indexμ(L,N,p) is different from zero. Then arbitrarily close to the branchpthere are intersection points ofL t such that N does not belong top.
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Ciriza, E., Pejsachowicz, J. (2000). A Bifurcation Theorem for Lagrangian Intersections. In: Appell, J. (eds) Recent Trends in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 40. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8411-2_12
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