Ivrii's conjecture for some cases in outer and symplectic billiards

We give a proof for $ (2n + 1, n) $ and $ (2n, n-1) $-periodic Ivrii's conjecture for planar outer billiards. We also give new simple geometric proofs for the 3 and 4-periodic cases for outer and symplectic billiards, and generalize for higher dimensions in case of symplectic billiards.

Authors

Publication Details

Journal
Discrete and Continuous Dynamical Systems
Published
2024-09-06
DOI
https://doi.org/10.3934/dcds.2024117
Primary Topic
Mathematical Dynamics and Fractals
Type
article
Field-Weighted Citation Impact
0.00

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article

Ivrii's conjecture for some cases in outer and symplectic billiards

Anastasiia Sharipova
Discrete and Continuous Dynamical Systems
Mathematical Dynamics and Fractals
article

Ivrii's conjecture for some cases in outer and symplectic billiards

Anastasiia Sharipova
article en

Abstract

We give a proof for $ (2n + 1, n) $ and $ (2n, n-1) $-periodic Ivrii's conjecture for planar outer billiards. We also give new simple geometric proofs for the 3 and 4-periodic cases for outer and symplectic billiards, and generalize for higher dimensions in case of symplectic billiards.

Discrete and Continuous Dynamical SystemsVol. 45(3)
National Science Foundation, Deutsche Forschungsgemeinschaft
Openalex Percentile: Top 74%
Mathematical Dynamics and Fractals
DOIOpen Access PDFOpenAlex
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Ivrii's conjecture for some cases in outer and symplectic billiards — Anastasiia Sharipova · Discrete and Continuous Dynamical Systems (2024) | TGRS Research Map | TGRS