Details

Subject(s)

• Convex domains [Browse]
• Affine differential geometry [Browse]
• Hamiltonian systems [Browse]
• Toric varieties [Browse]

Author

• Wacheux, Christophe [Browse]
• Nguyen, Tien Zung [Browse]

Series

• Memoirs of the American Mathematical Society ; no. 1424. [More in this series]
• Memoirs of the American Mathematical Society, 0065-9266 ; number 1424 [More in this 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.

Show 4 more Contents items

ISBN

• 9781470464394 ((paperback))
• 147046439X ((paperback))

LCCN

2023031262

OCLC

1393205949

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