A Bernoulli toral linked twist map without positive Lyapunov exponents
Nicol, Matthew (1996) A Bernoulli toral linked twist map without positive Lyapunov exponents Proceedings of the American Mathematical Society, 124. pp. 12531263.

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Abstract
<p>The presence of positive Lyapunov exponents in a dynamical system is often taken to be equivalent to the chaotic behavior of that system. We construct a Bernoulli toral linked twist map which has positive Lyapunov exponents and local stable and unstable manifolds defined only on a set of measure zero. This is a deterministic dynamical system with the strongest stochastic property, yet it has positive Lyapunov exponents only on a set of measure zero. In fact we show that for any map <i><b>g</i></b> in a certain class of piecewise linear Bernoulli toral linked twist maps, given any <b>epsilon > 0</b> there is a Bernoulli toral linked twist map <i><b>g'</i></b> with positive Lyapunov exponents defined only on a set of measure zero such that <i><b>g'</i></b> is within <b>epsilon</b> of <i><b>g</i></b> in the <i><b>d</i></b> metric.</p>
Item Type:  Article 

Additional Information:  First published in Proceedings of the American Mathematical Society, 124, 12531263. Published by the American Mathematical Society. © 1996 American Mathematical Society. 
Uncontrolled Keywords:  Lyapunov exponent, linked twist map 
Divisions:  Faculty of Engineering and Physical Sciences > Mathematics 
Depositing User:  Mr Adam Field 
Date Deposited:  27 May 2010 14:42 
Last Modified:  23 Sep 2013 18:33 
URI:  http://epubs.surrey.ac.uk/id/eprint/1545 
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