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Baker,s Map

المؤلف:  Lichtenberg, A. and Lieberman, M

المصدر:  Regular and Stochastic Motion. New York: Springer-Verlag

الجزء والصفحة:  ...

6-10-2021

1885

Baker's Map

The map

(1)

where  is computed modulo 1. A generalized Baker's map can be defined as

		{lambda_ax_n y_n<alpha ; (1-lambda_b)+lambda_bx_n y_n>alpha " src="https://mathworld.wolfram.com/images/equations/BakersMap/Inline4.gif" style="height:41px; width:146px" />	(2)
		{(y_n)/alpha y_n<alpha ; (y_n-alpha)/beta y_n>alpha," src="https://mathworld.wolfram.com/images/equations/BakersMap/Inline7.gif" style="height:78px; width:101px" />	(3)

where , , and  and  are computed mod 1. The  q-dimension is

(4)

If , then the general q-dimension is

(5)

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REFERENCES:

Lichtenberg, A. and Lieberman, M. Regular and Stochastic Motion. New York: Springer-Verlag, p. 60, 1983.

Ott, E. Chaos in Dynamical Systems. Cambridge, England: Cambridge University Press, pp. 81-82, 1993.

Rasband, S. N. Chaotic Dynamics of Nonlinear Systems. New York: Wiley, p. 32, 1990.