Devil's Staircase

A plot of the Winding Number resulting from Mode Locking as a function of for the Circle Map with . At each value of , the Winding Number issome Rational Number. The result is a monotonic increasing ``staircase'' for which the simplest RationalNumbers have the largest steps. For , the Measure of quasiperiodic states (Irrational) on the -axis has become zero, and the measure of Mode-Locked state has become 1. The Dimension of the Devil's staircase .

References

Mandelbrot, B. B. The Fractal Geometry of Nature. New York: W. H. Freeman, 1983.

Ott, E. Chaos in Dynamical Systems. New York: Cambridge University Press, 1993.

Rasband, S. N. Chaotic Dynamics of Nonlinear Systems. New York: Wiley, p. 132, 1990.

• Minimax Approximation
• Minimax Polynomial
• Minimax Theorem
• Minimum
• Minkowski-Bouligand Dimension
• Minkowski Convex Body Theorem
• Minkowski Geometry
• Minkowski-Hlawka Theorem
• Minkowski Integral Inequality
• Minkowski Measure
• Minkowski Metric
• Minkowski Sausage
• Minkowski Space
• Minkowski Sum
• Minkowski Sum Inequality
• Minor
• Minor Axis
• Minor Graph
• Minus
• Minus or Plus
• Minus Sign
• Minute
• Miquel Circles
• Miquel Equation
• Miquel Point