---
_id: '8416'
abstract:
- lang: eng
  text: In this paper, we show that any smooth one-parameter deformations of a strictly
    convex integrable billiard table Ω0 preserving the integrability near the boundary
    have to be tangent to a finite dimensional space passing through Ω0.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guan
  full_name: Huang, Guan
  last_name: Huang
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
citation:
  ama: Huang G, Kaloshin V. On the finite dimensionality of integrable deformations
    of strictly convex integrable billiard tables. <i>Moscow Mathematical Journal</i>.
    2019;19(2):307-327. doi:<a href="https://doi.org/10.17323/1609-4514-2019-19-2-307-327">10.17323/1609-4514-2019-19-2-307-327</a>
  apa: Huang, G., &#38; Kaloshin, V. (2019). On the finite dimensionality of integrable
    deformations of strictly convex integrable billiard tables. <i>Moscow Mathematical
    Journal</i>. American Mathematical Society. <a href="https://doi.org/10.17323/1609-4514-2019-19-2-307-327">https://doi.org/10.17323/1609-4514-2019-19-2-307-327</a>
  chicago: Huang, Guan, and Vadim Kaloshin. “On the Finite Dimensionality of Integrable
    Deformations of Strictly Convex Integrable Billiard Tables.” <i>Moscow Mathematical
    Journal</i>. American Mathematical Society, 2019. <a href="https://doi.org/10.17323/1609-4514-2019-19-2-307-327">https://doi.org/10.17323/1609-4514-2019-19-2-307-327</a>.
  ieee: G. Huang and V. Kaloshin, “On the finite dimensionality of integrable deformations
    of strictly convex integrable billiard tables,” <i>Moscow Mathematical Journal</i>,
    vol. 19, no. 2. American Mathematical Society, pp. 307–327, 2019.
  ista: Huang G, Kaloshin V. 2019. On the finite dimensionality of integrable deformations
    of strictly convex integrable billiard tables. Moscow Mathematical Journal. 19(2),
    307–327.
  mla: Huang, Guan, and Vadim Kaloshin. “On the Finite Dimensionality of Integrable
    Deformations of Strictly Convex Integrable Billiard Tables.” <i>Moscow Mathematical
    Journal</i>, vol. 19, no. 2, American Mathematical Society, 2019, pp. 307–27,
    doi:<a href="https://doi.org/10.17323/1609-4514-2019-19-2-307-327">10.17323/1609-4514-2019-19-2-307-327</a>.
  short: G. Huang, V. Kaloshin, Moscow Mathematical Journal 19 (2019) 307–327.
date_created: 2020-09-17T10:41:36Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '01'
doi: 10.17323/1609-4514-2019-19-2-307-327
extern: '1'
external_id:
  arxiv:
  - '1809.09341'
intvolume: '        19'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1809.09341
month: '04'
oa: 1
oa_version: Preprint
page: 307-327
publication: Moscow Mathematical Journal
publication_identifier:
  issn:
  - 1609-4514
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: On the finite dimensionality of integrable deformations of strictly convex
  integrable billiard tables
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2019'
...
---
_id: '8501'
abstract:
- lang: eng
  text: In this paper, we study small perturbations of a class of non-convex integrable
    Hamiltonians with two degrees of freedom, and we prove a result of diffusion for
    an open and dense set of perturbations, with an optimal time of diffusion which
    grows linearly with respect to the inverse of the size of the perturbation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Abed
  full_name: Bounemoura, Abed
  last_name: Bounemoura
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
citation:
  ama: Bounemoura A, Kaloshin V. Generic fast diffusion for a class of non-convex
    Hamiltonians with two degrees of freedom. <i>Moscow Mathematical Journal</i>.
    2014;14(2):181-203. doi:<a href="https://doi.org/10.17323/1609-4514-2014-14-2-181-203">10.17323/1609-4514-2014-14-2-181-203</a>
  apa: Bounemoura, A., &#38; Kaloshin, V. (2014). Generic fast diffusion for a class
    of non-convex Hamiltonians with two degrees of freedom. <i>Moscow Mathematical
    Journal</i>. Independent University of Moscow. <a href="https://doi.org/10.17323/1609-4514-2014-14-2-181-203">https://doi.org/10.17323/1609-4514-2014-14-2-181-203</a>
  chicago: Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class
    of Non-Convex Hamiltonians with Two Degrees of Freedom.” <i>Moscow Mathematical
    Journal</i>. Independent University of Moscow, 2014. <a href="https://doi.org/10.17323/1609-4514-2014-14-2-181-203">https://doi.org/10.17323/1609-4514-2014-14-2-181-203</a>.
  ieee: A. Bounemoura and V. Kaloshin, “Generic fast diffusion for a class of non-convex
    Hamiltonians with two degrees of freedom,” <i>Moscow Mathematical Journal</i>,
    vol. 14, no. 2. Independent University of Moscow, pp. 181–203, 2014.
  ista: Bounemoura A, Kaloshin V. 2014. Generic fast diffusion for a class of non-convex
    Hamiltonians with two degrees of freedom. Moscow Mathematical Journal. 14(2),
    181–203.
  mla: Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class of
    Non-Convex Hamiltonians with Two Degrees of Freedom.” <i>Moscow Mathematical Journal</i>,
    vol. 14, no. 2, Independent University of Moscow, 2014, pp. 181–203, doi:<a href="https://doi.org/10.17323/1609-4514-2014-14-2-181-203">10.17323/1609-4514-2014-14-2-181-203</a>.
  short: A. Bounemoura, V. Kaloshin, Moscow Mathematical Journal 14 (2014) 181–203.
date_created: 2020-09-18T10:47:09Z
date_published: 2014-04-01T00:00:00Z
date_updated: 2021-01-12T08:19:43Z
day: '01'
doi: 10.17323/1609-4514-2014-14-2-181-203
extern: '1'
external_id:
  arxiv:
  - '1304.3050'
intvolume: '        14'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
month: '04'
oa_version: Preprint
page: 181-203
publication: Moscow Mathematical Journal
publication_identifier:
  issn:
  - 1609-3321
  - 1609-4514
publication_status: published
publisher: Independent University of Moscow
quality_controlled: '1'
status: public
title: Generic fast diffusion for a class of non-convex Hamiltonians with two degrees
  of freedom
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2014'
...