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Comptes Rendus Mathématique
Volume 339, n° 5
pages 365-370 (septembre 2004)
Doi : 10.1016/j.crma.2004.06.024
Received : 17 June 2004 ;  accepted : 22 June 2004
Wandering triangles exist
L'existence des triangles errants.
 

Alexander Blokh 1 , Lex Oversteegen
Department of Mathematics, UAB, Birmingham, AL 35294, USA 

Abstract

W.P. Thurston introduced closed  -invariant laminations (where  ,  ) as a tool in complex dynamics. He defined wandering triangles as triples   such that   consists of three distinct points for all   and the convex hulls of all the sets   in the plane are pairwise disjoint, and proved that   admits no wandering triangles. We show that for every   there exist uncountably many  -invariant closed laminations with wandering triangles and pairwise non-conjugate factor maps of   on the corresponding quotient spaces. To cite this article: A. Blokh, L. Oversteegen, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
Résumé

Les laminations fermées  -invariantes (où  ) ont été introduites par W. P. Thurston comme un outil pour l'étude des systèmes dynamiques dans le plan complexe. Il avait défini les triangles errants comme étant des triplets   tels que   est composé des trois points distincts pour tout  , et les enveloppes convexes de tous les ensembles   sont deux-à-deux disjointes dans le plan complexe. Il avait démontré que   n'admet pas des triangles errants. Nous montrons que pour tout   il existe une collection nondénombrable de laminations fermées  -invariantes qui ont des triangles errants et des applications-facteurs de   non-conjuguées, deux-à-deux distinctes, sur les espaces quotients associés. Pour citer cet article : A. Blokh, L. Oversteegen, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
1  Recherche partiellment supportée par NSF Grant DMS 0140349.


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