Convexity of singular affine structures and toric-focus integrable Hamiltonian systems / Tudor S. Ratiu, Christophe Wacheux, Nguyen Tien Zung.

Author
Rațiu, Tudor S. [Browse]
Format
Book
Language
English
Published/​Created
  • Providence, RI : American Mathematical Society, 2023.
  • ©2023
Description
iv, 89 pages : illustrations ; 26 cm.

Details

Subject(s)
Author
Series
Summary note
"This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds (with boundary and corners), analogous to the toric case, but their associated integral affine structures are singular, with non-trivial monodromy, due to focus singularities. We obtain a series of convexity results, both positive and negative, for such singular integral affine base spaces. In particular, near a focus singular point, they are locally convex and the local-global convexity principle still applies. They are also globally convex under some natural additional conditions. However, when the monodromy is sufficiently large, the local-global convexity principle breaks down and the base spaces can be globally non-convex, even for compact manifolds. As a surprising example, we construct a 2-dimensional "integral affine black hole", which is locally convex but for which a straight ray from the center can never escape"-- Provided by publisher.
Notes
"July 2023, volume 287, number 1424 (second of 6 numbers)."
Bibliographic references
Includes bibliographical references (pages 79-86) and index.
Contents
  • Chapter 1. Introduction
  • Chapter 2. A brief overview of convexity in symplectic geometry and in integrable Hamiltonian systems
  • Chapter 3. Toric-focus integrable Hamiltonian systems
  • Chapter 4. Base spaces and affine manifolds with focus singularities
  • Chapter 5. Straight lines and convexity
  • Chapter 6. Local convexity at focus points
  • Chapter 7. Global convexity.
ISBN
  • 9781470464394 ((paperback))
  • 147046439X ((paperback))
LCCN
2023031262
OCLC
1393205949
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