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Invariant sets for discontinuous parabolic area-preserving torus maps

Ashwin, Peter, Fu, Xin-Chu, Nishkawa, Takashi and Zyczkowski, Karol (2000) Invariant sets for discontinuous parabolic area-preserving torus maps Nonlinearity, 13. pp. 819-835.


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We analyse a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two-parameter family of maps, the set of non-invertible maps is open and dense. For cases where the entries in the matrix are rational we show that the maximal invariant set has positive Lebesgue measure and we give bounds on the measure. For several examples we find expressions for the measure of the invariant set but we leave open the question as to whether there are parameters for which this measure is zero.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Ashwin, Peter
Fu, Xin-Chu
Nishkawa, Takashi
Zyczkowski, Karol
Date : 4 January 2000
Additional Information : This is a pre-copy-editing, author-prepared, peer-reviewed PDF of an article accepted for publication in Nonlinearity. The article appeared in Nonlinearity, 13, 819-835. © 2000 IOP Publishing Ltd. Click here to visit the journal website.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:40
Last Modified : 31 Oct 2017 14:01

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