15 February 2015 Prime ends rotation numbers and periodic points
Andres Koropecki, Patrice Le Calvez, Meysam Nassiri
Duke Math. J. 164(3): 403-472 (15 February 2015). DOI: 10.1215/00127094-2861386


We study the problem of existence of a periodic point in the boundary of an invariant domain for a surface homeomorphism. In the area-preserving setting, a complete classification is given in terms of rationality of Carathéodory’s prime ends rotation number, similar to Poincaré’s theory for circle homeomorphisms. In particular, we prove the converse of a classic result of Cartwright and Littlewood. The results are proved in a general context for homeomorphisms of arbitrary surfaces with a weak nonwandering-type hypothesis, which allows for applications in several different settings. The most important consequences are in the Cr-generic area-preserving context, building on previous work of Mather.


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Andres Koropecki. Patrice Le Calvez. Meysam Nassiri. "Prime ends rotation numbers and periodic points." Duke Math. J. 164 (3) 403 - 472, 15 February 2015. https://doi.org/10.1215/00127094-2861386


Published: 15 February 2015
First available in Project Euclid: 17 February 2015

zbMATH: 1382.37043
MathSciNet: MR3314477
Digital Object Identifier: 10.1215/00127094-2861386

Primary: 37E30
Secondary: 30D40 , 37B45 , 37E45

Keywords: boundary dynamics , dynamics of surface homeomorphisms , generic area-preserving diffeomorphisms , Periodic points , Primes ends , rotation numbers

Rights: Copyright © 2015 Duke University Press

Vol.164 • No. 3 • 15 February 2015
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