article published yes Luca Baracco author Olga Bernardi author Alessandra Nardi author 3e9c89df-ff0c-11f0-9fd7-c11e36d36769 VaKa department 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]. American Institute of Mathematical Sciences2026 eng 1930-5311 1930-532X 2410.1264410.3934/jmd.2026012 22469-488 L. Baracco, O. Bernardi, A. Nardi, Journal of Modern Dynamics 22 (2026) 469–488. 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> 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. 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>. 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> 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>. Baracco L, Bernardi O, Nardi A. 2026. Area spectral rigidity for axially symmetric symplectic billiard tables. Journal of Modern Dynamics. 22, 469–488. 229532026-09-17T11:05:53Z2026-09-24T12:12:44Z