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Starting the study of
outer length billiards
Luca Baracco, Olga Bernardi and Corentin Fierobe |
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Vol. 339 (2025), No. 2, 201–222
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Abstract |
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We focus on outer length billiard dynamics, acting on the exterior of a strictly convex planar domain. We first show that ellipses are totally integrable. We then provide an explicit representation of first order terms for the formal Taylor expansion of the corresponding Mather’s -function. Finally, we provide explicit Lazutkin coordinates up to order 4. |
Keywords
monotone twist maps, mathematical billiards, Mather beta
function, geometric approximations
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Mathematical Subject Classification
Primary: 37E40
Secondary: 37C83
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Milestones
Received: 8 May 2025
Revised: 8 September 2025
Accepted: 8 September 2025
Published: 21 September 2025
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Authors |
| Luca Baracco | |
| University of Padova Italy |
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| Olga Bernardi | |
| University of Padova Italy |
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| Corentin Fierobe | |
| University of Rome “Tor
Vergata” Italy |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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