@article{8426,
  abstract     = {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.},
  author       = {Buhovsky, Lev and Kaloshin, Vadim},
  issn         = {1560-3547},
  journal      = {Regular and Chaotic Dynamics},
  pages        = {54--59},
  publisher    = {Springer Nature},
  title        = {{Nonisometric domains with the same Marvizi-Melrose invariants}},
  doi          = {10.1134/s1560354718010057},
  volume       = {23},
  year         = {2018},
}