{"article_type":"original","status":"public","extern":"1","oa_version":"None","page":"76-90","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0081-5438","1531-8605"]},"year":"2009","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."}],"publisher":"Springer Nature","quality_controlled":"1","language":[{"iso":"eng"}],"issue":"1","intvolume":"       267","keyword":["Mathematics (miscellaneous)"],"article_processing_charge":"No","volume":267,"_id":"8508","doi":"10.1134/s0081543809040063","title":"Conservative homoclinic bifurcations and some applications","author":[{"first_name":"Anton","last_name":"Gorodetski","full_name":"Gorodetski, Anton"},{"first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","full_name":"Kaloshin, Vadim"}],"date_updated":"2021-01-12T08:19:46Z","month":"12","type":"journal_article","citation":{"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>.","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>","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>","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.","short":"A. Gorodetski, V. Kaloshin, Proceedings of the Steklov Institute of Mathematics 267 (2009) 76–90.","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>."},"publication":"Proceedings of the Steklov Institute of Mathematics","date_created":"2020-09-18T10:48:03Z","publication_status":"published","day":"01","date_published":"2009-12-01T00:00:00Z"}