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FIZIKA B 6 (1997) 1, 23-35
 
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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