6.D.6. IFS Driven by Dynamical Systems

Trapping Square

A trapping square is small square, with opposite corners on the line y = x, having two properties:
the iterates of almost every starting point eventually enters the trapping square, and
once the iterates enter the trapping square, they never leave.
For example,
Iterates enter the trapping square Iterates never leave the trapping square
For functions L(x) that increase to their maximum value (at x = 1/2, say) and then decrease, the trapping square is defined by the values L(1/2) and L2(1/2). Here is an illustration.

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