The Geometry of the Group of Symplectic Diffeomorphism is popular PDF and ePub book, written by Leonid Polterovich in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Geometry of the Group of Symplectic Diffeomorphism can be Read Online from any device for your convenience.
The Geometry of the Group of Symplectic Diffeomorphism Book PDF Summary
The group of Hamiltonian diffeomorphisms Ham(M, 0) of a symplectic mani fold (M, 0) plays a fundamental role both in geometry and classical mechanics. For a geometer, at least under some assumptions on the manifold M, this is just the connected component of the identity in the group of all symplectic diffeomorphisms. From the viewpoint of mechanics, Ham(M,O) is the group of all admissible motions. What is the minimal amount of energy required in order to generate a given Hamiltonian diffeomorphism I? An attempt to formalize and answer this natural question has led H. Hofer [HI] (1990) to a remarkable discovery. It turns out that the solution of this variational problem can be interpreted as a geometric quantity, namely as the distance between I and the identity transformation. Moreover this distance is associated to a canonical biinvariant metric on Ham(M, 0). Since Hofer's work this new ge ometry has been intensively studied in the framework of modern symplectic topology. In the present book I will describe some of these developments. Hofer's geometry enables us to study various notions and problems which come from the familiar finite dimensional geometry in the context of the group of Hamiltonian diffeomorphisms. They turn out to be very different from the usual circle of problems considered in symplectic topology and thus extend significantly our vision of the symplectic world.
Detail Book of The Geometry of the Group of Symplectic Diffeomorphism PDF
- Author : Leonid Polterovich
- Release : 06 December 2012
- Publisher : Birkhäuser
- ISBN : 9783034882996
- Genre : Mathematics
- Total Page : 138 pages
- Language : English
- PDF File Size : 12,7 Mb
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