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The paper concerns a -rigidity result for the characteristic foliations in symplectic geometry. A symplectic homeomorphism (in the sense of Eliashberg-Gromov) which preserves a smooth hypersurface also preserves its characteristic foliation.
In this short paper, we show that the only proper holomorphic self-maps of bounded domains in whose iterates approach a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type theorem for a sequence of maps whose degrees are unbounded.
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