First Steps Towards a Symplectic Dynamics by Barney Bramham, Helmut Hofer - Free PDF
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About this book :-
A long time ago, these two fields - symplectic geometry (which comes from physics and helps describe the shape of space) and dynamical systems (which studies how things move or evolve) were closely connected. But over the years, they drifted apart. Bramham and Hofer believe now is the right time to bring them back together, and they have some powerful tools to do it.
Both dynamical systems and symplectic geometry have rich theories and the time seems ripe to develop the common core with integrated ideas from both fields. Barney Bramham and Helmut Hofer explore an exciting idea: blending the study of geometry and motion in a new, more unified way. They call this new approach Symplectic Dynamics. The text discuss problems which show how dynamical systems questions and symplectic ideas come together in a nontrivial way.
Book Detail :-
This book has following details information.
Title:
First Steps Towards a Symplectic Dynamics by Barney Bramham, Helmut Hofer - Free PDF
Publisher:
arXiv
Year:
2011
Pages:
60
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
N\A
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About Author :-
The author NA
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Book Contents :-
This book has following table of contents.
1. What Should Symplectic Dynamics be?
2. Holomorphic Curves
2.1 Contact Forms and Holomorphic Curves
2.2 Notions of Energy
2.3 Global Systems of Surfaces of Section
3. Holomorphic Curves and Disk Maps
3.1 Reeb-like Mapping Tori
3.2 Notions of rotation number
3.3 Finite Energy Foliations for Mapping Tori
3.4 A Proof of the Poincar´e-Birkhoff Fixed Point Theorem
3.5 A Proof of a Theorem of Franks and Handel
4. Asymptotic Foliations for Disk Maps
4.1 Detecting Invariant Circles
4.2 Speculations on Pseudo-Rotations
4.3 Questions
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