--- _id: '8426' 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. article_processing_charge: No article_type: original author: - first_name: Lev full_name: Buhovsky, Lev last_name: Buhovsky - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 citation: ama: Buhovsky L, Kaloshin V. Nonisometric domains with the same Marvizi-Melrose invariants. Regular and Chaotic Dynamics. 2018;23:54-59. doi:10.1134/s1560354718010057 apa: Buhovsky, L., & Kaloshin, V. (2018). Nonisometric domains with the same Marvizi-Melrose invariants. Regular and Chaotic Dynamics. Springer Nature. https://doi.org/10.1134/s1560354718010057 chicago: Buhovsky, Lev, and Vadim Kaloshin. “Nonisometric Domains with the Same Marvizi-Melrose Invariants.” Regular and Chaotic Dynamics. Springer Nature, 2018. https://doi.org/10.1134/s1560354718010057. ieee: L. Buhovsky and V. Kaloshin, “Nonisometric domains with the same Marvizi-Melrose invariants,” Regular and Chaotic Dynamics, vol. 23. Springer Nature, pp. 54–59, 2018. ista: Buhovsky L, Kaloshin V. 2018. Nonisometric domains with the same Marvizi-Melrose invariants. Regular and Chaotic Dynamics. 23, 54–59. mla: Buhovsky, Lev, and Vadim Kaloshin. “Nonisometric Domains with the Same Marvizi-Melrose Invariants.” Regular and Chaotic Dynamics, vol. 23, Springer Nature, 2018, pp. 54–59, doi:10.1134/s1560354718010057. short: L. Buhovsky, V. Kaloshin, Regular and Chaotic Dynamics 23 (2018) 54–59. date_created: 2020-09-17T10:43:21Z date_published: 2018-02-05T00:00:00Z date_updated: 2021-01-12T08:19:11Z day: '05' doi: 10.1134/s1560354718010057 extern: '1' external_id: arxiv: - '1801.00952' intvolume: ' 23' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1801.00952 month: '02' oa: 1 oa_version: Preprint page: 54-59 publication: Regular and Chaotic Dynamics publication_identifier: issn: - 1560-3547 - 1468-4845 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Nonisometric domains with the same Marvizi-Melrose invariants type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 23 year: '2018' ...