Control of transient chaos in tent maps near crisis. I. Fixed point targeting

Combinatorial techniques are applied to the symbolic dynamics representing transient chaotic behavior in tent maps in order to solve the problem of Ott-Grebogi-Yorke control to the nontrivial fixed point occurring in such maps. This approach allows "preimage overlap" to be treated exactly. Closed forms for both the probability of control being achieved and the average number of iterations to control are derived. The results are discussed in relation to the work of Tel and shed new light on the transition to the control of permanent chaos.