Charles Micchelli
Journal of Approximation Theory
The decimal expansion of real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history through a partition. But in order to get a useful symbolism, one needs to construct a partition with special properties. In this work we develop a general theory of representing dynamical systems by symbolic systems by means of so-called Markov partitions. We apply the results to one of the more tractable examples: namely, hyperbolic automorphisms of the two dimensional torus. While there are some results in higher dimensions, this area remains a fertile one for research.
Charles Micchelli
Journal of Approximation Theory
Guo-Jun Qi, Charu Aggarwal, et al.
IEEE TPAMI
Zhihua Xiong, Yixin Xu, et al.
International Journal of Modelling, Identification and Control
W.F. Cody, H.M. Gladney, et al.
SPIE Medical Imaging 1994