Area spectral rigidity for axially symmetric symplectic billiard tables Baracco, Luca Bernardi, Olga Nardi, Alessandra 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 Sciences 2026 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22953 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> eng info:eu-repo/semantics/altIdentifier/doi/10.3934/jmd.2026012 info:eu-repo/semantics/altIdentifier/issn/1930-5311 info:eu-repo/semantics/altIdentifier/e-issn/1930-532X info:eu-repo/semantics/altIdentifier/arxiv/2410.12644 info:eu-repo/semantics/openAccess