# Finite Lyapunov Exponent for Generalized Logistic Maps with *z*-Unimodality

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This Demonstration shows a finite Lyapunov exponent of a one-dimensional unimodal map , which is a generalization of the well-known logistic map . The related Lyapunov exponent can be defined by

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Contributed by: Ki-Jung Moon (January 2014)

Based on a program by: Stephen Wolfram

Open content licensed under CC BY-NC-SA

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References

[1] S. H. Strogatz, *Nonlinear Dynamics and Chaos*, New York: Perseus Books Publishing, 1994.

[2] K. T. Alligood, T. D. Sauer, and J. A. Yorke, *Chaos: An Introduction to Dynamical Systems*, New York: Springer, 1996.

[3] H.-O. Peitgen, H. Jürgens, and D. Saupe, *Chaos and Fractals: New Frontiers of Science*, 2nd ed., New York: Springer, 2004.

[4] S. Wolfram, *A New Kind of Science*, Champaign, IL: Wolfram Media, 2002.

[5] M. J. Feigenbaum, "Quantitative Universality for a Class of Non-Linear Transformations," *Journal of Statistical Physics*, 19, 1978 pp. 25–52.

[6] M. J. Feigenbaum, "The Universal Metric Properties of Nonlinear Transformations," *Journal of Statistical Physics*, 21, 1979 pp. 669–706.

[7] K.-J. Moon, "Reducible Expansions and Related Sharp Crossovers in Feigenbaum's Renormalization Field," *Chaos: An Interdisciplinary Journal of Nonlinear Science*, 18, 2008 pp. 023104.

[8] K.-J. Moon, "Erratum: Reducible Expansions and Related Sharp Crossovers in Feigenbaum's Renormalization Field," *Chaos: An Interdisciplinary Journal of Nonlinear Science*, 20, 2010 pp. 049902.

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