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2012.59: Families of piecewise linear maps with constant Lyapunov exponent

2012.59: V Botella-Soler, J A Oteo, J Ros and P Glendinning (2012) Families of piecewise linear maps with constant Lyapunov exponent.

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We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.

Item Type:MIMS Preprint
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Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MIMS number:2012.59
Deposited By:Professor Paul Glendinning
Deposited On:24 May 2012

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