From Periodic Motion to Unbounded Chaos: Investigations of the Simple Pendulum

Leo P Kadanoff
1985 Physica Scripta  
The simplest example of the onset of chaos in a Hamiltonian system is provided by the "standard" or Chirikov-Taylor model. As a nonlinearity parameter, k , is increased the long term behavior of the momentum, p , is examined. At k = 0, p is conserved. For k < k" for all startingpoints,p is of bounded variation. For some starting points its behavior is periodic, for others quasi-periodic, for others chaotic. At some critical value of k , unbounded chaotic variation first appears. A scaling
more » ... rs. A scaling analysis to describe this onset is described.
doi:10.1088/0031-8949/1985/t9/001 fatcat:63bezxfznvdwdmjveqqzr3xvsq