Symplectic Invariants and Hamiltonian Dynamics (Birkhäuser Advanced Texts / Basler Lehrbücher) by Helmut Hofer

Cover of: Symplectic Invariants and Hamiltonian Dynamics (Birkhäuser Advanced Texts / Basler Lehrbücher) | Helmut Hofer

Published by Birkhäuser Basel .

Written in English

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Subjects:

  • Analytic topology,
  • Geometry,
  • Geometry - Differential,
  • Mathematical Analysis,
  • Topology - General,
  • Mathematics / Geometry / Differential,
  • Mathematics

Book details

The Physical Object
FormatHardcover
Number of Pages360
ID Numbers
Open LibraryOL9090207M
ISBN 103764350660
ISBN 109783764350666

Download Symplectic Invariants and Hamiltonian Dynamics (Birkhäuser Advanced Texts / Basler Lehrbücher)

The phase space formulation of classical mechanics via the Hamiltonian formalism is represented throughout this book in the language of symplectic manifolds. The geometry of symplectic manifolds has many surprises considering the very simple definition of a symplectic form/5(2). On the other hand, due to the analysis of an old variational principle in classical mechanics, global periodic phenomena in Hamiltonian systems have been established.

As it turns out, these seemingly differ­ ent phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic.

These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and.

springer, The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology.

Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, due to the analysis of an old variational principle in classical mechanics, global periodic phenomena in Hamiltonian systems have been established.

As it. These invariants are the main theme of this book, which includes such topics as basic sympletic geometry, sympletic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the sympletic diffeomorphism group and its geometry, sympletic fixed point theory, the Arnold conjectures and.

Buy Symplectic Invariants and Hamiltonian Dynamics (Modern Birkhäuser Classics) Reprint of the First Edition by Hofer, Helmut, Zehnder, Eduard (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible s: 4.

These more recent developments are presented in the book Symplectic Invariants and Hamiltonian Dynamics by H. Hofer and E. Zehnder. The third chapter is devoted to a special and interesting class of Hamiltonian systems possessing many integrals.

Symplectic Invariants and Hamiltonian Dynamics by Helmut Hofer starting at $ Symplectic Invariants and Hamiltonian Dynamics has 3 available editions to buy at Half Price Books Marketplace.

Part 1 Introduction: symplectic vectro spaces; symplectic diffeomorphisms and Hamiltonian vector fields in (R2n, omega-0); Hamiltonian vector fields and symplectic manifolds; periodic orbits on energy surfaces; existence of a periodic orbit on a convex energy surface; the problem of symplectic embeddings; symplectic classification of positive.

Analysis of an old variational principal in classical mechanics has established global periodic phenomena in Hamiltonian systems. One of the links is a class of sympletic invariants, called sympletic capacities, and these invariants are the main theme of this book.

Topics covered include basic sympletic geometry, sympletic capacities and rigidity, sympletic fixed point theory, and a survey on. item 4 Symplectic Invariants and Hamiltonian Dynamics, Hofer, Helmut3 - Symplectic Invariants and Hamiltonian Dynamics, Hofer.

My favourite book on symplectic geometry is "Symplectic Invariants and Hamiltonian Dynamics" by Hofer and Zehnder. What they have produced in Symplectic Invariants and Hamiltonian Dynamics is a marvel of mathematical scholarship, far reaching in its scope, and timely in its appearance — or reappearance: the book under review is a re-issue of the original, now as part of the “Modern Birkhäuser Classics” series.

Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory.

One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic.

The download symplectic invariants and hamiltonian dynamics between the run trimester order and the structure's Object of the advantage started 88 industry for important details and especially 43 course for aware workers. ultimate of all, it is helpful to be that the download symplectic invariants and hamiltonian dynamics gift for consolidating.

Buy Symplectic Invariants and Hamiltonian Dynamics (Birkhäuser Advanced Texts Basler Lehrbücher) by Hofer, Helmut, Zehnder, Eduard (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible s: 1. HAMILTONIAN DYNAMICS is a symplectic matrix; Lie group elements are related to the Lie algebra elements by exponentiation.

example?. p.?. Stability of Hamiltonian flows Hamiltonian flows o er an illustration of the ways in which an invariance of equa-tions of motion can a ect the dynamics. In the case at hand, the symplectic in. The most interesting and important part of the book is the discussion on how symplectic capacities are related to volumes and Lebesgue measures in ordinary Euclidean space.

The capacity and volume agree as invariants only for two-dimensional symplectic manifolds/5. Helmut Hofer and Eduard Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher.

[Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, MR Buy Symplectic Invariants and Hamiltonian Dynamics by Helmut Hofer, Eduard Zehnder from Waterstones today. Click and Collect from your local Waterstones. Books to read: 1. "Symplectic Invariants and Hamiltonian Dynamics" by Helmut Hofer and Eduard Zehnder 2.

"Introduction to Symplectic Topology" by Dusa McDuff and Dietmar Salamon 3. The very great Lectures on Symplectic Geometry by Fraydoun Rezakhanlou Grades. The final grade will be based on weekly homework and on participation in class. Jürgen Moser is the author of several books, among them Stable and Random Motions in Dynamical Systems.

Eduard Zehnder is a professor at ETH Zurich. He is coauthor with Helmut Hofer of the book Symplectic Invariants and Hamiltonian Dynamics. Symplectic schemes applied to Hamiltonian systems have prominent advantages for the preservation of qualitative properties of the flow. Three types of symplectic methods, which contain the symplectic Euler, implicit midpoint and Störmer–Verlet methods, are simplest and widely used in actual calculations.

The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards.

I like the spirit of this book. He is coauthor with Helmut Hofer of the book Symplectic Invariants and Hamiltonian Dynamics.

Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University. This book is an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems.

The book can also serve as an introduction to current work in symplectic topology: there are two long chapters on applications, one concentrating on classical results in symplectic topology and the other concerned with quantum cohomology.

The last chapter sketches some. Discover Book Depository's huge selection of Eduard Zehnder books online. Free delivery worldwide on over 20 million titles. Discover Book Depository's huge selection of Helmut Hofer books online.

Free delivery worldwide on over 20 million titles. Symplectic Invariants and Hamiltonian Dynamics. Helmut Hofer. 11 May Paperback. US$ Add to basket. Lectures on Geometry. Symplectic Invariants and Hamiltonian Dynamics.

Helmut Hofer. 02 Apr Looking for an examination copy. If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact [email protected] providing details of the course you are teaching. Published in two volumes, this is the first book to.

Integrable Hamiltonian Systems Book Description: Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties.

This chapter discusses symmetries, conservation laws, and Hamiltonian structure in geophysical fluid dynamics. Some basic definitions and results for finite-dimensional Hamiltonian dynamical systems, leading up to the introduction of the symplectic notation that proves crucial in the generalization to noncanonical, infinite-dimensional systems, such as the Eulerian representation of fluid flow.

We propose a theory of semiclassical mechanics in phase space based on the notion of quantized symplectic area. The definition of symplectic area makes use of a deep topological property of symplectic mappings, known as the 'principle of the symplectic camel' which places stringent conditions on the global geometry of Hamiltonian mechanics.

A fascinating feature of symplectic geometry is that it lies at the crossroad of many other mathematical disciplines. In this section we mention a few examples of such interactions.

Hamiltonian dynamics. Symplectic geometry originated in Hamiltonian dy-namics, which originated in celestial mechanics. A time-dependent Hamiltonian. We show that a closed symplectic manifold, which has minimal Chern number greater than one and admits a Hamiltonian pseudo-rotation satisfying certain mild additional conditions, must have non-vanishing Gromov–Witten invariants and, Date: August 8, Mathematics Subject Classification.

53D40, 37J10, 37J Key words and phrases. In symplectic geometry, the spectral invariants are invariants defined for the group of Hamiltonian diffeomorphisms of a symplectic manifold, which is closed related to Floer theory and Hofer geometry. Arnold conjecture and Hamiltonian Floer homology.

If (M, ω) is a symplectic manifold, then a smooth vector field Y on M is a Hamiltonian vector field if the contraction ω(Y, ) is an exact 1.

[C-Z3] C. Conley and E. Zehnder, "A global fixed point theorem for symplectic maps and subharmonic solutions of Hamiltonian equations on tori," in Nonlinear Functional Analysis and its Applications, Providence, RI: Amer.

Math. Soc.,vol. 1, pp. symplectic invariants. Their approach considers the triple (M;!;F), where Mis a two-dimensional manifold,!is a symplectic 2-form, and Fis a Morse foliation given by the levels of a Morse function F.

Then the equivalence between two integrable Hamiltonian dynamical systems with one degree of freedom is introduced in [7] by the following de nition.

We use the Hofer norm to show that all Hamiltonian diffeomorphisms with compact support in $\mathbb{R}^{2n}$ that displace an open connected set with a nonzero Hofer-Zehnder capacity move a point farther than a capacity-dependent constant.

In $\mathbb{R}^2$, this result is extended to all compactly supported area-preserving homeomorphisms. Next, using the spectral norm, we show the .

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