文摘
英文文摘
前言
Chapter 1 The completions of Hamiltonian diffeomorphisms
1.1 Introduction and the main results
1.2 Preliminaries in Symplectic Geometry
1.3 Hamiltonian Homeomorphisms
1.4 Induced Hamiltonian homeomorphisms on the symplectic quotient
1.5 The completions of Hamiltonian diffeomorphisms under Viterbo metric
1.6 Appendix：The Viterbo metric
Chapter 2 L∞-norm on the strictly contact diffeomorphisms
2.1 Introduction and the main results
2.2 Contact diffeomorphisms and Banyaga's metric
2.3 Proof of the main theorem
2.4 The group of strictly contact homeomorphisms
Chapter 3 A Hofer-type norm of Hamiltonian maps on regular Poisson manifolds
3.1 Introduction and the main results
3.2 The Hofer-type norm of Hamiltonian maps on regular Poisson manifolds
3.3 Proof of Theorem 12
3.4 Geodesics in Ham(M)on regular Poisson manifolds
3.5 The Hofer-type norm of Hamiltonian maps under Poisson reduction
3.6 The Hamiltonian homeomorphisms on regular Poisson manifolds
Bibliography
致谢
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