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Zero-dimensional singular continuous spectrum for smooth differential equations on the torus

Hof, A. and Knill, O. (1998) Zero-dimensional singular continuous spectrum for smooth differential equations on the torus. Ergodic Theory and Dynamical Systems, 18 (4). pp. 879-888. ISSN 0143-3857. http://resolver.caltech.edu/CaltechAUTHORS:20111222-080337837

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Abstract

We study spectral properties of the flow x = 1/F(x,y), y = 1/λF(x,y) on the 2-torus. We show that, in general, the speed of approximation in cyclic approximation gives an upper bound on the Hausdorff dimension of the supports of spectral measures. We use this to prove that for generic pairs (F,λ) the spectrum of the flow on the torus is singular continuous with all spectral measures supported on sets of zero Hausdorff dimension.


Item Type:Article
Related URLs:
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http://dx.doi.org/10.1017/S0143385798117467 DOIUNSPECIFIED
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=32435PublisherUNSPECIFIED
Additional Information:© 1998 Cambridge University Press. Received 14 September 1996 and accepted in revised form 24 July 1997. Published online: 08 September 2000.
Record Number:CaltechAUTHORS:20111222-080337837
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111222-080337837
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28557
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jan 2012 19:53
Last Modified:26 Dec 2012 14:38

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