Periodic Estimation of the 3-Arnold Transformation Modulo N
We discuss the basic definitions and existing conclusion about periodicity of the twin Fibonacci sequence in this paper. The upper bound of the twin Fibonacci sequence and the least period of 3-dimensional Arnold transformation mod N are respectively 6.269N2 and 3.134N2, which is similar to two existing references. Moreover, many important properties are gained, which provide new thought for study on the period of higher-dimensional Arnold transformation and the necessary mathematical reference of image coding and processing.
Wenya Tian and Linli Xu
Y. J. Li et al., "Periodic Estimation of the 3-Arnold Transformation Modulo N", Advanced Materials Research, Vol. 186, pp. 515-519, 2011