Lyapunov exponent and topological entropy plateaus in piecewise linear maps

V. Botella Soler, J. Oteo, J. Ros, P. Glendinning, Journal of Physics A: Mathematical and Theoretical 46 (2013) 125101.

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Journal Article | Published | English
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Abstract
We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.
Publishing Year
Date Published
2013-03-29
Journal Title
Journal of Physics A: Mathematical and Theoretical
Volume
46
Issue
12
Article Number
125101
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Botella Soler V, Oteo J, Ros J, Glendinning P. Lyapunov exponent and topological entropy plateaus in piecewise linear maps. Journal of Physics A: Mathematical and Theoretical. 2013;46(12):125101. doi:10.1088/1751-8113/46/12/125101
Botella Soler, V., Oteo, J., Ros, J., & Glendinning, P. (2013). Lyapunov exponent and topological entropy plateaus in piecewise linear maps. Journal of Physics A: Mathematical and Theoretical, 46(12), 125101. https://doi.org/10.1088/1751-8113/46/12/125101
Botella Soler, Vicente, José Oteo, Javier Ros, and Paul Glendinning. “Lyapunov Exponent and Topological Entropy Plateaus in Piecewise Linear Maps.” Journal of Physics A: Mathematical and Theoretical 46, no. 12 (2013): 125101. https://doi.org/10.1088/1751-8113/46/12/125101.
V. Botella Soler, J. Oteo, J. Ros, and P. Glendinning, “Lyapunov exponent and topological entropy plateaus in piecewise linear maps,” Journal of Physics A: Mathematical and Theoretical, vol. 46, no. 12, p. 125101, 2013.
Botella Soler V, Oteo J, Ros J, Glendinning P. 2013. Lyapunov exponent and topological entropy plateaus in piecewise linear maps. Journal of Physics A: Mathematical and Theoretical. 46(12), 125101.
Botella Soler, Vicente, et al. “Lyapunov Exponent and Topological Entropy Plateaus in Piecewise Linear Maps.” Journal of Physics A: Mathematical and Theoretical, vol. 46, no. 12, IOP Publishing Ltd., 2013, p. 125101, doi:10.1088/1751-8113/46/12/125101.

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