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.

• Cartesian Trident
• Cartography
• Cascade
• Casey's Theorem
• Casimir Operator
• Cassini Ellipses
• Cassini Ovals
• Cassini Projection
• Cassini's Identity
• Cassini Surface
• Castillon's Problem
• Casting Out Nines
• Catacaustic
• Catalan Integrals
• Catalan Number
• Catalan's Conjecture
• Catalan's Constant
• Catalan's Diophantine Problem
• Catalan Solid
• Catalan's Problem
• Catalan's Surface
• Catalan's Triangle
• Catalan's Trisectrix
• Catastrophe
• Catastrophe Theory