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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Consider a sequence of compactly supported Hamiltonian diffeomorphisms $\phi_k$ of an exact symplectic manifold, all of which are ``graphical'' in the sense that their graphs are identified by a Darboux-Weinstein chart with the image of a one-form. We show by an elementary argument that if the $\phi_k$ $C^0$-converge to the identity, then their Calabi invariants converge to zero. This generalizes a result of Oh, in which the ambient manifold was the two-disk and an additional assumption was made on the Hamiltonians generating the $\phi_k$. We discuss connections to the open problem of whether the Calabi homomorphism extends to the Hamiltonian homeomorphism group. The proof is based on a relationship between the Calabi invariant of a $C^0$-small Hamiltonian diffeomorphism and the generalized phase function of its graph.
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참고문헌 (10)
참고문헌 신청
A. Banyaga / 1978 / Sur la structure du groupe des diffeomorphismes qui preservent une forme symplectique / Comment. Math. Helv 53 (2) : 174 ~ 227
C. Viterbo / 2006 / On the uniqueness of generating Hamiltonian for continuous limits of Hamiltonians ows / Int. Math. Res. Not 2006 : 9 ~
E. Calabi / 1970 / On the group of automorphisms of a symplectic manifold / Problems in analysis (Lectures at the Sympos. in honor of Salomon Bochner, Princeton Univ., Princeton, N
J.-C. Sikorav / 1987 / Problemes d'intersections et de points xes en g eom etrie hamiltonienne / Comment. Math. Helv 62 (1) : 62 ~ 73
L. Buhovsky / 2013 / Uniqueness of generating Hamiltonians for topological Hamiltonian ows / J. Symplectic Geom 11 (1) : 37 ~ 52
C. Viterbo / 2006 / On the uniqueness of generating Hamiltonian for continuous limits of Hamiltonians ows / Int. Math. Res. Not 2006 : 9 ~
E. Calabi / 1970 / On the group of automorphisms of a symplectic manifold / Problems in analysis (Lectures at the Sympos. in honor of Salomon Bochner, Princeton Univ., Princeton, N
J.-C. Sikorav / 1987 / Problemes d'intersections et de points xes en g eom etrie hamiltonienne / Comment. Math. Helv 62 (1) : 62 ~ 73
L. Buhovsky / 2013 / Uniqueness of generating Hamiltonians for topological Hamiltonian ows / J. Symplectic Geom 11 (1) : 37 ~ 52
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