اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Hofer-like metric on the group of symplectic diffeomorphisms
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تأليف
Augustin Banyaga
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Using a Hodge decomposition of symplectic isotopies on a compact symplectic manifold $(M,omega)$, we construct a norm on the identity component in the group of all symplectic diffeomorphisms of $(M,omega)$ whose restriction to the group $Ham(M,omega)$ of hamiltonian diffeomorphisms is bounded from above by the Hofer norm. Moreover, $Ham(M,omega)$ is closed in $Symp(M,omega)$ equipped with the topology induced by the extended norm. We give an application to the $C^0$ symplectic topology. We also discuss extensions of Ohs spectral distance.
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