A NOTE ON HOFER'S NORM

Title & Authors
A NOTE ON HOFER'S NORM
Cho, Yong-Seung; Kwak, Jin-Ho; Yoon, Jin-Yue;

Abstract
We Show that When ($\small{M,\;\omega}$) is a closed, simply connected, symplectic manifold for all $\small{\gamma\;\in\;\pi_1(Ham(M),\;id)}$ the following inequality holds: $\small{\parallel\gamma\parallel\;{\geq}\;sup_{\={x}}\;|A(\={x})|,\;where\;\parallel\gamma\parallel}$ is the coarse Hofer's norm, $\small{\={x}}$ run over all extensions to $\small{D^2}$ of an orbit $\small{x(t)\;=\;{\varphi}_t(z)}$ of a fixed point $\small{z\;\in\;M,\;A(\={x})}$ the symplectic action of $\small{\={x}}$, and the Hamiltonian diffeomorphisms {$\small{{\varphi}_t}$} of M represent $\small{\gamma}$.
Keywords
symplectic mnifold;Hamiltonian diffeomorphism;coarse Hofer′s norm;symplectic action;coupling form;
Language
English
Cited by
1.
NOTES ON THE SPACE OF DIRICHLET TYPE AND WEIGHTED BESOV SPACE,;

충청수학회지, 2013. vol.26. 2, pp.393-402
References
1.
V. Guillemin, E. Lerman, and S. Sternberg, Symplectic Fibrations and Multiplicity Diagrams, Cambridge University Press, 1996.

2.
D. McDuff and D. Salamon, Introduction to Symplectic Topology, Clarendon Press, Oxford, 1995.

3.
L. Polterovich, Hamiltonian loops and Arnold's principle, Amer. Math. Soc.Transl. Ser 2, 180 (1997), 181-187.