Fractal Structure of Subharmonic Steps in Dissipative Systems Described by a Driven Damped Pendulum Equation
Since it became clear that the return map for the driven damped pendulum equationwith I(ø) = sinø at and below the transition to chaos is a circle map for every irrational rotation number W,1 the connection between the scaling laws for the pendulum system and the structures obtained by iterations of circle maps has been studied extensively. In particular, the universal scaling behavior of the complete devil’s staircase obtained by iterations of circle maps2 like the sine mapwith a zero slope third order inflection point has been conjectured also to be found at the transition to chaos in every dissipative dynamical system with two competing frequencies.3
KeywordsRotation Number Dissipative System Critical Line Pendulum System Dissipative Dynamical System
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© Springer Science+Business Media New York 1991