---
_id: '8508'
abstract:
- lang: eng
  text: We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving
    diffeomorphisms (conservative New house phenomena) and show that they give rise
    to invariant hyperbolic sets of arbitrarily large Hausdorff dimension. As applications,
    we discuss the size of the stochastic layer of a standard map and the Hausdorff
    dimension of invariant hyperbolic sets for certain restricted three-body problems.
    We avoid involved technical details and only concentrate on the ideas of the proof
    of the presented results.
article_processing_charge: No
article_type: original
author:
- first_name: Anton
  full_name: Gorodetski, Anton
  last_name: Gorodetski
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
citation:
  ama: Gorodetski A, Kaloshin V. Conservative homoclinic bifurcations and some applications.
    <i>Proceedings of the Steklov Institute of Mathematics</i>. 2009;267(1):76-90.
    doi:<a href="https://doi.org/10.1134/s0081543809040063">10.1134/s0081543809040063</a>
  apa: Gorodetski, A., &#38; Kaloshin, V. (2009). Conservative homoclinic bifurcations
    and some applications. <i>Proceedings of the Steklov Institute of Mathematics</i>.
    Springer Nature. <a href="https://doi.org/10.1134/s0081543809040063">https://doi.org/10.1134/s0081543809040063</a>
  chicago: Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations
    and Some Applications.” <i>Proceedings of the Steklov Institute of Mathematics</i>.
    Springer Nature, 2009. <a href="https://doi.org/10.1134/s0081543809040063">https://doi.org/10.1134/s0081543809040063</a>.
  ieee: A. Gorodetski and V. Kaloshin, “Conservative homoclinic bifurcations and some
    applications,” <i>Proceedings of the Steklov Institute of Mathematics</i>, vol.
    267, no. 1. Springer Nature, pp. 76–90, 2009.
  ista: Gorodetski A, Kaloshin V. 2009. Conservative homoclinic bifurcations and some
    applications. Proceedings of the Steklov Institute of Mathematics. 267(1), 76–90.
  mla: Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations
    and Some Applications.” <i>Proceedings of the Steklov Institute of Mathematics</i>,
    vol. 267, no. 1, Springer Nature, 2009, pp. 76–90, doi:<a href="https://doi.org/10.1134/s0081543809040063">10.1134/s0081543809040063</a>.
  short: A. Gorodetski, V. Kaloshin, Proceedings of the Steklov Institute of Mathematics
    267 (2009) 76–90.
date_created: 2020-09-18T10:48:03Z
date_published: 2009-12-01T00:00:00Z
date_updated: 2021-01-12T08:19:46Z
day: '01'
doi: 10.1134/s0081543809040063
extern: '1'
intvolume: '       267'
issue: '1'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
month: '12'
oa_version: None
page: 76-90
publication: Proceedings of the Steklov Institute of Mathematics
publication_identifier:
  issn:
  - 0081-5438
  - 1531-8605
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Conservative homoclinic bifurcations and some applications
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 267
year: '2009'
...