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Izvestiya: Mathematics, 2006, Volume 70, Issue 6, Pages 1093–1116
DOI: https://doi.org/10.1070/IM2006v070n06ABEH002340 (Mi im678) 		 
This article is cited in 19 scientific papers (total in 19 papers)

The regularity of central leaves of partially hyperbolic sets and its applications

A. S. Gorodetski

California Institute of Technology
English version PDF (408 kB) Citations (19)
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DOI: https://doi.org/10.1070/IM2006v070n06ABEH002340
Abstract: We consider partially hyperbolic maps which are close to the direct product of a hyperbolic map and an identity map and prove that their central leaves depend Hölder continuously on the base point in the $C^r$-metric. We use this result to construct an open set of diffeomorphisms with rather unusual properties (they have transitive sets with periodic points of different indices and orbits with zero Lyapunov exponent). This paper concludes a series of joint papers with Yu. S. Ilyashenko.
Received: 11.07.2001
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2006, Volume 70, Issue 6, Pages 19–44
DOI: https://doi.org/10.4213/im678
Bibliographic databases:
UDC: 517.938
MSC: 37D30, 37C20
Language: English
Original paper language: Russian
Citation: A. S. Gorodetski, “The regularity of central leaves of partially hyperbolic sets and its applications”, Izv. RAN. Ser. Mat., 70:6 (2006), 19–44; Izv. Math., 70:6 (2006), 1093–1116
Citation in format AMSBIB
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    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:542
    Russian version PDF:189
    English version PDF:13
    References:83
    First page:4
     
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