[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"22953","title":"Area spectral rigidity for axially symmetric symplectic billiard tables","day":"24","page":"469-488","arxiv":1,"publication_identifier":{"issn":["1930-5311"],"eissn":["1930-532X"]},"department":[{"_id":"VaKa"}],"supplementarymaterial":"no","fulldoi":"https://doi.org/10.3934/jmd.2026012","mathsc":["37D50","53C24","58J53"],"researchdata_availability":"no","doi":"10.3934/jmd.2026012","oa":1,"corr_author":"1","das_tickbox":"0","article_type":"original","external_id":{"arxiv":["2410.12644"]},"article_processing_charge":"No","volume":22,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.12644"}],"quality_controlled":"1","status":"public","OA_place":"repository","type":"journal_article","language":[{"iso":"eng"}],"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]."}],"author":[{"first_name":"Luca","last_name":"Baracco","full_name":"Baracco, Luca"},{"first_name":"Olga","last_name":"Bernardi","full_name":"Bernardi, Olga"},{"last_name":"Nardi","first_name":"Alessandra","full_name":"Nardi, Alessandra","id":"3e9c89df-ff0c-11f0-9fd7-c11e36d36769"}],"OA_type":"green","scopus_import":"1","date_updated":"2026-09-24T12:12:44Z","publication_status":"published","year":"2026","date_created":"2026-09-17T11:05:53Z","publication":"Journal of Modern Dynamics","intvolume":"        22","publisher":"American Institute of Mathematical Sciences","month":"07","date_published":"2026-07-24T00:00:00Z","oa_version":"Preprint","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>","ista":"Baracco L, Bernardi O, Nardi A. 2026. Area spectral rigidity for axially symmetric symplectic billiard tables. Journal of Modern Dynamics. 22, 469–488.","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.","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>","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>.","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>.","short":"L. Baracco, O. Bernardi, A. Nardi, Journal of Modern Dynamics 22 (2026) 469–488."}}]