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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 267, Pages 82–96 (Mi tm2596)  
This article is cited in 3 scientific papers (total in 3 papers)

Conservative Homoclinic Bifurcations and Some Applications

A. Gorodetskia, V. Kaloshinb

a Department of Mathematics, University of California, Irvine, CA, USA
b Department of Mathematics, Penn State University, State College, PA, USA
Full-text PDF (272 kB) Citations (3)
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Abstract: We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving diffeomorphisms (conservative Newhouse 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.
Received in April 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2009, Volume 267, Pages 76–90
DOI: https://doi.org/10.1134/S0081543809040063
Bibliographic databases:
UDC: 517.938
Language: English
Citation: A. Gorodetski, V. Kaloshin, “Conservative Homoclinic Bifurcations and Some Applications”, Singularities and applications, Collected papers, Trudy Mat. Inst. Steklova, 267, MAIK Nauka/Interperiodica, Moscow, 2009, 82–96; Proc. Steklov Inst. Math., 267 (2009), 76–90
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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