Optimization of real phase-mask performance
F.M. Schellenberg, M. Levenson, et al.
BACUS Symposium on Photomask Technology and Management 1991
We study Markov chains via invariants constructed from periodic orbits. Canonical extensions, based on these invariants, are used to establish a constraint on the degree of finite-to-one block homomorphisms from one Markov chain to another. We construct a polytope from the normalized weights of periodic orbits. Using this polytope, we find canonically-defined induced Markov chains inside the original Markov chain. Each of the invariants associated with these Markov chains gives rise to a scaffold of invariants for the original Markov chain. This is used to obtain counterexamples to the finite equivalence conjecture and to a conjecture regarding finitary isomorphism with finite expected coding time. Also included are results related to the problem of minimality (with respect to block homomorphism) of Bernoulli shifts in the class of Markov chains with beta function equal to the beta function of the Bernoulli shift. © 1991, Cambridge University Press. All rights reserved.
F.M. Schellenberg, M. Levenson, et al.
BACUS Symposium on Photomask Technology and Management 1991
Michael E. Henderson
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Robert Manson Sawko, Malgorzata Zimon
SIAM/ASA JUQ
Jonathan Ashley, Brian Marcus, et al.
Ergodic Theory and Dynamical Systems