Polterovich, Leonid 1963
Overview
Works:  8 works in 30 publications in 1 language and 405 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor 
Classifications:  QA649, 516.36 
Publication Timeline
.
Most widely held works by
Leonid Polterovich
The geometry of the group of symplectic diffeomorphism
by
Leonid Polterovich(
Book
)
13 editions published between 2000 and 2001 in English and held by 228 WorldCat member libraries worldwide
The group of symplectic diffeomorphisms of a symplectic manifold plays a fundamental role both in geometry and classical mechanics. What is the minimal amount of energy required in order to generate a given mechanical motion? This variational problem admits an interpretation in terms of a remarkable geometry on the group discovered by Hofer in 1990. Hofer's geometry serves as a source of interesting problems and gives rise to new methods and notions which extend significantly our vision of the symplectic world. In the past decade this new geometry has been intensively studied in the framework of symplectic topology with the use of modern techniques such as Gromov's theory of pseudoholomorphic curves, Floer homology and GuilleminSternbergLerman theory of symplectic connections. Furthermore, it opens up the intriguing prospect of using an alternative geometric intuition in dynamics. The book provides an essentially selfcontained introduction into these developments and includes recent results on diameter, geodesics and growth of oneparameter subgroups in Hofer's geometry, as well as applications to dynamics and ergodic theory. It is addressed to researchers and students from the graduate level onwards
13 editions published between 2000 and 2001 in English and held by 228 WorldCat member libraries worldwide
The group of symplectic diffeomorphisms of a symplectic manifold plays a fundamental role both in geometry and classical mechanics. What is the minimal amount of energy required in order to generate a given mechanical motion? This variational problem admits an interpretation in terms of a remarkable geometry on the group discovered by Hofer in 1990. Hofer's geometry serves as a source of interesting problems and gives rise to new methods and notions which extend significantly our vision of the symplectic world. In the past decade this new geometry has been intensively studied in the framework of symplectic topology with the use of modern techniques such as Gromov's theory of pseudoholomorphic curves, Floer homology and GuilleminSternbergLerman theory of symplectic connections. Furthermore, it opens up the intriguing prospect of using an alternative geometric intuition in dynamics. The book provides an essentially selfcontained introduction into these developments and includes recent results on diameter, geodesics and growth of oneparameter subgroups in Hofer's geometry, as well as applications to dynamics and ergodic theory. It is addressed to researchers and students from the graduate level onwards
New perspectives and challenges in symplectic field theory
(
Book
)
4 editions published in 2009 in English and held by 99 WorldCat member libraries worldwide
4 editions published in 2009 in English and held by 99 WorldCat member libraries worldwide
Function theory on symplectic manifolds
by
Leonid Polterovich(
Book
)
3 editions published in 2014 in English and held by 49 WorldCat member libraries worldwide
3 editions published in 2014 in English and held by 49 WorldCat member libraries worldwide
Geometries in interaction : GAFA special issue in honor of Mikhail Gromov
by
Y Eliashberg(
)
4 editions published in 1995 in English and held by 24 WorldCat member libraries worldwide
Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. PiatetskiShapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics
4 editions published in 1995 in English and held by 24 WorldCat member libraries worldwide
Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. PiatetskiShapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics
Topology invariants of Lagrange Embeddings and Hamiltonian dynamics
by
Leonid Polterovich(
Book
)
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
Boundary rigidity for Lagrangian submanifolds, nonremovable intersections, and AubryMather theory
(
)
2 editions published in 2003 in English and held by 1 WorldCat member library worldwide
2 editions published in 2003 in English and held by 1 WorldCat member library worldwide
Transversal Hamiltonian fields and differential relations
by
Leonid Polterovich(
Book
)
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
Symplectic displacement energy for Lagrangian submanifolds
by
Leonid Polterovich(
Book
)
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
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