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-- part contents for background part 22
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Period-doubling is the process where, as a physical parameter is varied, a limit cycle of the system (or a fixed point of a map), with 
• frequency  f,  period  T=2π/f,  loses stability to a limit cycle of 
•  frequency  f/2,  period  2T,  which later loses stability to a limit cycle of
•  frequency  f/4,  period  4T,  which later loses stability to a limt cycle of
•  frequency  f/8,  period  8T,  which . . .