---
_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'
...