[{"page":"3287-3301","date_updated":"2026-06-18T17:54:16Z","main_file_link":[{"url":"https://doi.org/10.3934/dcds.2024059","open_access":"1"}],"day":"01","OA_type":"free access","external_id":{"isi":["001230091000001"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","corr_author":"1","quality_controlled":"1","oa":1,"publisher":"American Institute of Mathematical Sciences","author":[{"first_name":"Corentin","id":"06619f18-9070-11eb-847d-d1ee780bd88b","last_name":"Fiorebe","full_name":"Fiorebe, Corentin"}],"_id":"17231","ddc":["500"],"doi":"10.3934/dcds.2024059","type":"journal_article","scopus_import":"1","language":[{"iso":"eng"}],"publication":"Discrete and Continuous Dynamical Systems- Series A","date_published":"2024-11-01T00:00:00Z","year":"2024","intvolume":"        44","issue":"11","publication_identifier":{"issn":["1078-0947"],"eissn":["1553-5231"]},"title":"Examples of projective billiards with open sets of periodic orbits","status":"public","department":[{"_id":"VaKa"}],"article_processing_charge":"No","isi":1,"volume":44,"abstract":[{"text":"In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter-examples are polygons admitting a 2-parameters family of n-periodic orbits, with n being either 3 or any even integer greater than 4.","lang":"eng"}],"month":"11","article_type":"original","date_created":"2024-07-14T22:01:10Z","citation":{"ista":"Fiorebe C. 2024. Examples of projective billiards with open sets of periodic orbits. Discrete and Continuous Dynamical Systems- Series A. 44(11), 3287–3301.","ieee":"C. Fiorebe, “Examples of projective billiards with open sets of periodic orbits,” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 44, no. 11. American Institute of Mathematical Sciences, pp. 3287–3301, 2024.","mla":"Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic Orbits.” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 44, no. 11, American Institute of Mathematical Sciences, 2024, pp. 3287–301, doi:<a href=\"https://doi.org/10.3934/dcds.2024059\">10.3934/dcds.2024059</a>.","apa":"Fiorebe, C. (2024). Examples of projective billiards with open sets of periodic orbits. <i>Discrete and Continuous Dynamical Systems- Series A</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/dcds.2024059\">https://doi.org/10.3934/dcds.2024059</a>","chicago":"Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic Orbits.” <i>Discrete and Continuous Dynamical Systems- Series A</i>. American Institute of Mathematical Sciences, 2024. <a href=\"https://doi.org/10.3934/dcds.2024059\">https://doi.org/10.3934/dcds.2024059</a>.","ama":"Fiorebe C. Examples of projective billiards with open sets of periodic orbits. <i>Discrete and Continuous Dynamical Systems- Series A</i>. 2024;44(11):3287-3301. doi:<a href=\"https://doi.org/10.3934/dcds.2024059\">10.3934/dcds.2024059</a>","short":"C. Fiorebe, Discrete and Continuous Dynamical Systems- Series A 44 (2024) 3287–3301."},"oa_version":"Published Version"},{"quality_controlled":"1","publication_status":"published","author":[{"first_name":"Rowan","last_name":"Killip","full_name":"Killip, Rowan"},{"first_name":"Satoshi","last_name":"Masaki","full_name":"Masaki, Satoshi"},{"first_name":"Jason","full_name":"Murphy, Jason","last_name":"Murphy"},{"last_name":"Visan","full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"_id":"22030","publisher":"American Institute of Mathematical Sciences","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1804.06753"}],"date_updated":"2026-06-22T11:06:54Z","page":"553-583","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","OA_type":"green","external_id":{"arxiv":["1804.06753"]},"volume":39,"abstract":[{"lang":"eng","text":"We consider the mass-subcritical NLS in dimensions d>=3 with radial initial data. In the defocusing case, we prove that any solution that remains bounded in the critical Sobolev space throughout its lifespan must be global and scatter. In the focusing case, we prove the existence of a threshold solution that has a compact flow."}],"month":"01","article_processing_charge":"No","status":"public","oa_version":"Preprint","das_tickbox":"1","citation":{"apa":"Killip, R., Masaki, S., Murphy, J., &#38; Vişan, M. (2019). The radial mass-subcritical NLS in negative order Sobolev spaces. <i>Discrete and Continuous Dynamical Systems</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/dcds.2019023\">https://doi.org/10.3934/dcds.2019023</a>","mla":"Killip, Rowan, et al. “The Radial Mass-Subcritical NLS in Negative Order Sobolev Spaces.” <i>Discrete and Continuous Dynamical Systems</i>, vol. 39, no. 1, American Institute of Mathematical Sciences, 2019, pp. 553–83, doi:<a href=\"https://doi.org/10.3934/dcds.2019023\">10.3934/dcds.2019023</a>.","chicago":"Killip, Rowan, Satoshi Masaki, Jason Murphy, and Monica Vişan. “The Radial Mass-Subcritical NLS in Negative Order Sobolev Spaces.” <i>Discrete and Continuous Dynamical Systems</i>. American Institute of Mathematical Sciences, 2019. <a href=\"https://doi.org/10.3934/dcds.2019023\">https://doi.org/10.3934/dcds.2019023</a>.","ieee":"R. Killip, S. Masaki, J. Murphy, and M. Vişan, “The radial mass-subcritical NLS in negative order Sobolev spaces,” <i>Discrete and Continuous Dynamical Systems</i>, vol. 39, no. 1. American Institute of Mathematical Sciences, pp. 553–583, 2019.","ista":"Killip R, Masaki S, Murphy J, Vişan M. 2019. The radial mass-subcritical NLS in negative order Sobolev spaces. Discrete and Continuous Dynamical Systems. 39(1), 553–583.","ama":"Killip R, Masaki S, Murphy J, Vişan M. The radial mass-subcritical NLS in negative order Sobolev spaces. <i>Discrete and Continuous Dynamical Systems</i>. 2019;39(1):553-583. doi:<a href=\"https://doi.org/10.3934/dcds.2019023\">10.3934/dcds.2019023</a>","short":"R. Killip, S. Masaki, J. Murphy, M. Vişan, Discrete and Continuous Dynamical Systems 39 (2019) 553–583."},"OA_place":"repository","extern":"1","date_created":"2026-06-19T07:41:46Z","article_type":"original","language":[{"iso":"eng"}],"publication":"Discrete and Continuous Dynamical Systems","date_published":"2019-01-01T00:00:00Z","scopus_import":"1","type":"journal_article","doi":"10.3934/dcds.2019023","title":"The radial mass-subcritical NLS in negative order Sobolev spaces","publication_identifier":{"eissn":["1553-5231"],"issn":["1078-0947"]},"arxiv":1,"issue":"1","intvolume":"        39","year":"2019"},{"external_id":{"arxiv":["1509.05822"]},"OA_type":"green","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"3831-3866","date_updated":"2026-06-22T12:47:32Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1509.05822"}],"oa":1,"publisher":"American Institute of Mathematical Sciences","_id":"22033","author":[{"last_name":"Killip","full_name":"Killip, Rowan","first_name":"Rowan"},{"last_name":"Miao","full_name":"Miao, Changxing","first_name":"Changxing"},{"last_name":"Visan","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica"},{"last_name":"Zhang","full_name":"Zhang, Junyong","first_name":"Junyong"},{"first_name":"Jiqiang","full_name":"Zheng, Jiqiang","last_name":"Zheng"}],"publication_status":"published","quality_controlled":"1","intvolume":"        37","year":"2017","issue":"7","arxiv":1,"publication_identifier":{"eissn":["1553-5231"],"issn":["1078-0947"]},"title":"The energy-critical NLS with inverse-square potential","doi":"10.3934/dcds.2017162","type":"journal_article","publication":"Discrete and Continuous Dynamical Systems","language":[{"iso":"eng"}],"date_published":"2017-07-01T00:00:00Z","scopus_import":"1","article_type":"original","date_created":"2026-06-19T07:42:59Z","citation":{"ama":"Killip R, Miao C, Vişan M, Zhang J, Zheng J. The energy-critical NLS with inverse-square potential. <i>Discrete and Continuous Dynamical Systems</i>. 2017;37(7):3831-3866. doi:<a href=\"https://doi.org/10.3934/dcds.2017162\">10.3934/dcds.2017162</a>","short":"R. Killip, C. Miao, M. Vişan, J. Zhang, J. Zheng, Discrete and Continuous Dynamical Systems 37 (2017) 3831–3866.","ista":"Killip R, Miao C, Vişan M, Zhang J, Zheng J. 2017. The energy-critical NLS with inverse-square potential. Discrete and Continuous Dynamical Systems. 37(7), 3831–3866.","ieee":"R. Killip, C. Miao, M. Vişan, J. Zhang, and J. Zheng, “The energy-critical NLS with inverse-square potential,” <i>Discrete and Continuous Dynamical Systems</i>, vol. 37, no. 7. American Institute of Mathematical Sciences, pp. 3831–3866, 2017.","apa":"Killip, R., Miao, C., Vişan, M., Zhang, J., &#38; Zheng, J. (2017). The energy-critical NLS with inverse-square potential. <i>Discrete and Continuous Dynamical Systems</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/dcds.2017162\">https://doi.org/10.3934/dcds.2017162</a>","mla":"Killip, Rowan, et al. “The Energy-Critical NLS with Inverse-Square Potential.” <i>Discrete and Continuous Dynamical Systems</i>, vol. 37, no. 7, American Institute of Mathematical Sciences, 2017, pp. 3831–66, doi:<a href=\"https://doi.org/10.3934/dcds.2017162\">10.3934/dcds.2017162</a>.","chicago":"Killip, Rowan, Changxing Miao, Monica Vişan, Junyong Zhang, and Jiqiang Zheng. “The Energy-Critical NLS with Inverse-Square Potential.” <i>Discrete and Continuous Dynamical Systems</i>. American Institute of Mathematical Sciences, 2017. <a href=\"https://doi.org/10.3934/dcds.2017162\">https://doi.org/10.3934/dcds.2017162</a>."},"OA_place":"repository","extern":"1","oa_version":"Preprint","das_tickbox":"1","status":"public","month":"07","volume":37,"abstract":[{"text":"We consider the defocusing energy-critical nonlinear Schrödinger\r\nequation with inverse-square potential iut = −∆u + a|x|^−2u + |u|^4u in three\r\nspace dimensions. We prove global well-posedness and scattering for a >− 1/4 + 1/25. We also carry out the variational analysis needed to treat the focusing case.","lang":"eng"}],"article_processing_charge":"No"}]