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The group Hameo (M, ω) of Hamiltonian homeomorphisms
of a connected symplectic manifold (M, ω) was defined and studied in
[7] and further in [6]. In these papers, the authors consistently used
the L(¹,∞)-Hofer norm (and not the L∞-Hofer norm) on the space of
Hamiltonian paths (see below for the definitions). A justification for this
choice was given in [7]. In this article we study the L∞-case. In view of
the fact that the Hofer norm on the group Ham(M, ω) of Hamiltonian
diffeomorphisms does not depend on the choice of the L(¹,∞)-norm vs.
the L∞-norm [9], Y.-G. Oh and D. McDuff (private communications)
asked whether the two notions of Hamiltonian homeomorphisms arising
from the different norms coincide. We will give an affirmative answer to
this question in this paper.
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참고문헌 (10)
참고문헌 신청
C. Viterbo / 2006 / On the uniqueness of generating Hamiltonian for continuous limits of Hamiltonians flows / International Mathematics Research Notices : 9 ~
F. Lalonde / 1995 / The geometry of symplectic energy / Annals of Mathematics 141 (2) : 349 ~ 371
H. Hofer / 1990 / On the topological properties of symplectic maps / Proceedings of the Royal Society of Edinburgh Section: A Mathematics 115 (1) : 25 ~ 38
L. Polterovich / 1993 / Symplectic displacement energy for Lagrangian submanifolds / Ergodic Theory and Dynamical Systems 13 (2) : 357 ~ 367
L. Polterovich / 2001 / The Geometry of the Group of Symplectic Diffeomorphisms, Lectures in Mathematics ETH Zurich / Birkh¨auser Verlag
F. Lalonde / 1995 / The geometry of symplectic energy / Annals of Mathematics 141 (2) : 349 ~ 371
H. Hofer / 1990 / On the topological properties of symplectic maps / Proceedings of the Royal Society of Edinburgh Section: A Mathematics 115 (1) : 25 ~ 38
L. Polterovich / 1993 / Symplectic displacement energy for Lagrangian submanifolds / Ergodic Theory and Dynamical Systems 13 (2) : 357 ~ 367
L. Polterovich / 2001 / The Geometry of the Group of Symplectic Diffeomorphisms, Lectures in Mathematics ETH Zurich / Birkh¨auser Verlag
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