Hamurcu ve Arnold 'un Kedisi Transformasyonlarında Karşılaşılan Paradoksal Bulguların İncelenmesi

Abstract

Bakers’ map in one of the stretch, cut and fold procedure examples which represent a typical chaotic model with strange attractor. The Chaotic hehavior associated with exponential divergence of nearby trajectories can clearly be confirmed up to about 8 – 10 steps of iteration. On the other and computer appication exceeding 30-40 iterations exhibits completely different character that is no matter where behavior is explained by stuying X component of the map viz. Bernoulli shift.

In this respect Arnolds’ cat map is another example which deserves attention. In contrast to its strong mixing character, in digitalized form a Picture after mixing thoroughly fort he first 30th to 40th step in reapers in the orginal form and complete recurrence is abserved. It is shown that depending on pixel numbers used, the Picture may topple in halp period. An alternative cat map which we coined the name reversed cat map is also studied. It is interesting to see that a generalized form of the Bernoulli shift map can be used to obtain random time series which may be instrumental for Random number generators having uniform probability distribution.