MISSING PREIMAGES FOR CHAOTIC LOGISTIC MAP WITH A HOLE

VLADIMIR PAAR AND NENAD PAVIN

Department of Physics, Faculty of Science, University of Zagreb, Zagreb, Croatia

Received 19 November 1996

Chaotic transients and preimages are investigated for a new map proposed recently, having a hole in the unit interval of the r = 4 logistic map. This map is characterized by deviations from Frobenius-Perron equation for average lifetimes in dependence on hole position in the form of bursts of average lifetime. We present classification of these bursts on the basis of average lifetimes. Using time maps it is investigated how these bursts are caused by missing preimages of the hole interval I ^{( 0 )}. We derive approximate expression for the ratio of lifetimes deduced from Frobenius-Perron and from Kantz-Grassberger equations.

UDC 531.133
PACS 05.45.+b

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