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Sbornik: Mathematics, 2006, Volume 197, Issue 2, Pages 173–192
DOI: https://doi.org/10.1070/SM2006v197n02ABEH003752 (Mi sm1509) 		 
Closed cross-sections of irrational flows on surfaces

S. Kh. Aranson, I. A. Gorelikovaa, E. V. Zhuzhomaa

a Nizhny Novgorod State Technical University
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DOI: https://doi.org/10.1070/SM2006v197n02ABEH003752
Abstract: Simple closed transversals to an irrational flow on a closed surface with negative Euler characteristic are considered. A negative answer is given to A. Katok's conjecture about the existence of simple closed transversals to irrational flows on such surfaces in each free homotopy class containing simple closed curves non-homotopic to zero.
Bibliography: 17 titles.
Received: 25.01.2005
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 2, Pages 35–56
DOI: https://doi.org/10.4213/sm1509
Bibliographic databases:
UDC: 517.917+513.9
MSC: Primary 37E35; Secondary 37C10
Language: English
Original paper language: Russian
Citation: S. Kh. Aranson, I. A. Gorelikova, E. V. Zhuzhoma, “Closed cross-sections of irrational flows on surfaces”, Mat. Sb., 197:2 (2006), 35–56; Sb. Math., 197:2 (2006), 173–192
Citation in format AMSBIB
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    Russian version PDF:202
    English version PDF:6
    References:55
    First page:3
     
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