Families of piecewise linear maps with constant Lyapunov exponent

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

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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
Additional Information: CICADA
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
Depositing User: Professor Paul Glendinning
Date Deposited: 24 May 2012
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1835

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