---
OA_place: repository
OA_type: green
_id: '22953'
abstract:
- lang: eng
  text: We prove that any finitely smooth, axially symmetric, strictly convex domain
    with everywhere positive curvature and sufficiently close to an ellipse is area
    spectrally rigid. This means that any area-isospectral family of domains in this
    class is necessarily equi-affine. We use techniques, adapted to symplectic billiards,
    inspired by the paper of J. De Simoi, V. Kaloshin and Q. Wei [5].
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Luca
  full_name: Baracco, Luca
  last_name: Baracco
- first_name: Olga
  full_name: Bernardi, Olga
  last_name: Bernardi
- first_name: Alessandra
  full_name: Nardi, Alessandra
  id: 3e9c89df-ff0c-11f0-9fd7-c11e36d36769
  last_name: Nardi
citation:
  ama: Baracco L, Bernardi O, Nardi A. Area spectral rigidity for axially symmetric
    symplectic billiard tables. <i>Journal of Modern Dynamics</i>. 2026;22:469-488.
    doi:<a href="https://doi.org/10.3934/jmd.2026012">10.3934/jmd.2026012</a>
  apa: Baracco, L., Bernardi, O., &#38; Nardi, A. (2026). Area spectral rigidity for
    axially symmetric symplectic billiard tables. <i>Journal of Modern Dynamics</i>.
    American Institute of Mathematical Sciences. <a href="https://doi.org/10.3934/jmd.2026012">https://doi.org/10.3934/jmd.2026012</a>
  chicago: Baracco, Luca, Olga Bernardi, and Alessandra Nardi. “Area Spectral Rigidity
    for Axially Symmetric Symplectic Billiard Tables.” <i>Journal of Modern Dynamics</i>.
    American Institute of Mathematical Sciences, 2026. <a href="https://doi.org/10.3934/jmd.2026012">https://doi.org/10.3934/jmd.2026012</a>.
  ieee: L. Baracco, O. Bernardi, and A. Nardi, “Area spectral rigidity for axially
    symmetric symplectic billiard tables,” <i>Journal of Modern Dynamics</i>, vol.
    22. American Institute of Mathematical Sciences, pp. 469–488, 2026.
  ista: Baracco L, Bernardi O, Nardi A. 2026. Area spectral rigidity for axially symmetric
    symplectic billiard tables. Journal of Modern Dynamics. 22, 469–488.
  mla: Baracco, Luca, et al. “Area Spectral Rigidity for Axially Symmetric Symplectic
    Billiard Tables.” <i>Journal of Modern Dynamics</i>, vol. 22, American Institute
    of Mathematical Sciences, 2026, pp. 469–88, doi:<a href="https://doi.org/10.3934/jmd.2026012">10.3934/jmd.2026012</a>.
  short: L. Baracco, O. Bernardi, A. Nardi, Journal of Modern Dynamics 22 (2026) 469–488.
corr_author: '1'
das_tickbox: '0'
date_created: 2026-09-17T11:05:53Z
date_published: 2026-07-24T00:00:00Z
date_updated: 2026-09-24T12:12:44Z
day: '24'
department:
- _id: VaKa
doi: 10.3934/jmd.2026012
external_id:
  arxiv:
  - '2410.12644'
fulldoi: https://doi.org/10.3934/jmd.2026012
intvolume: '        22'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2410.12644
mathsc:
- 37D50
- 53C24
- 58J53
month: '07'
oa: 1
oa_version: Preprint
page: 469-488
publication: Journal of Modern Dynamics
publication_identifier:
  eissn:
  - 1930-532X
  issn:
  - 1930-5311
publication_status: published
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Area spectral rigidity for axially symmetric symplectic billiard tables
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 22
year: '2026'
...