---
_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
arxiv: 1
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. <i>Regular and Chaotic Dynamics</i>. 2018;23:54-59. doi:<a href="https://doi.org/10.1134/s1560354718010057">10.1134/s1560354718010057</a>
  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>
  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>.
  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.
  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.” <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>.
  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'
...