{"language":[{"iso":"eng"}],"_id":"8426","page":"54-59","month":"02","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","day":"05","extern":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1801.00952"}],"date_updated":"2021-01-12T08:19:11Z","publication_status":"published","external_id":{"arxiv":["1801.00952"]},"article_processing_charge":"No","title":"Nonisometric domains with the same Marvizi-Melrose invariants","article_type":"original","doi":"10.1134/s1560354718010057","abstract":[{"lang":"eng","text":"For any strictly convex planar domain Ω ⊂ R2 with a C∞ boundary one can associate an infinite sequence of spectral invariants introduced by Marvizi–Merlose [5]. These invariants can generically be determined using the spectrum of the Dirichlet problem of the Laplace operator. A natural question asks if this collection is sufficient to determine Ω up to isometry. In this paper we give a counterexample, namely, we present two nonisometric domains Ω and Ω¯ with the same collection of Marvizi–Melrose invariants. Moreover, each domain has countably many periodic orbits {Sn}n≥1 (resp. {S¯n}n⩾1) of period going to infinity such that Sn and S¯n have the same period and perimeter for each n."}],"oa":1,"date_created":"2020-09-17T10:43:21Z","publication_identifier":{"issn":["1560-3547","1468-4845"]},"intvolume":"        23","publisher":"Springer Nature","author":[{"first_name":"Lev","last_name":"Buhovsky","full_name":"Buhovsky, Lev"},{"orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"year":"2018","publication":"Regular and Chaotic Dynamics","type":"journal_article","volume":23,"date_published":"2018-02-05T00:00:00Z","citation":{"apa":"Buhovsky, L., &#38; Kaloshin, V. (2018). Nonisometric domains with the same Marvizi-Melrose invariants. <i>Regular and Chaotic Dynamics</i>. Springer Nature. <a href=\"https://doi.org/10.1134/s1560354718010057\">https://doi.org/10.1134/s1560354718010057</a>","mla":"Buhovsky, Lev, and Vadim Kaloshin. “Nonisometric Domains with the Same Marvizi-Melrose Invariants.” <i>Regular and Chaotic Dynamics</i>, vol. 23, Springer Nature, 2018, pp. 54–59, doi:<a href=\"https://doi.org/10.1134/s1560354718010057\">10.1134/s1560354718010057</a>.","ieee":"L. Buhovsky and V. Kaloshin, “Nonisometric domains with the same Marvizi-Melrose invariants,” <i>Regular and Chaotic Dynamics</i>, vol. 23. Springer Nature, pp. 54–59, 2018.","chicago":"Buhovsky, Lev, and Vadim Kaloshin. “Nonisometric Domains with the Same Marvizi-Melrose Invariants.” <i>Regular and Chaotic Dynamics</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1134/s1560354718010057\">https://doi.org/10.1134/s1560354718010057</a>.","short":"L. Buhovsky, V. Kaloshin, Regular and Chaotic Dynamics 23 (2018) 54–59.","ama":"Buhovsky L, Kaloshin V. Nonisometric domains with the same Marvizi-Melrose invariants. <i>Regular and Chaotic Dynamics</i>. 2018;23:54-59. doi:<a href=\"https://doi.org/10.1134/s1560354718010057\">10.1134/s1560354718010057</a>","ista":"Buhovsky L, Kaloshin V. 2018. Nonisometric domains with the same Marvizi-Melrose invariants. Regular and Chaotic Dynamics. 23, 54–59."},"oa_version":"Preprint","status":"public"}