Denjoy’s theorem with exponents-Reference-Cited by-同舟云学术

Denjoy’s theorem with exponents

Published:1999-04-23 Issue:10 Volume:127 Page:3111-3118
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Norton Alec

Abstract

If X X is the (unique) minimal set for a C 1 + α C^{1+\alpha } diffeomorphism of the circle without periodic orbits, 0 > α > 1 0>\alpha >1 , then the upper box dimension of X X is at least α \alpha . The method of proof is to introduce the exponent α \alpha into the proof of Denjoy’s theorem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1999-127-10/S0002-9939-99-04852-2/S0002-9939-99-04852-2.pdf

Reference15 articles.

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3. P. Bohl, Uber die hinsichtlich der unabhängigen variabeln periodische Differential gleichung erster Ordnung, Acta Math. 40 (1916), 321–336.

4. A. Denjoy, Sur les courbes definies par les equations differentielles a la surface du tore, J. Math Pures et Appl. 11 (1932), 333–375.

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