On Quantum Iterated Function Systems
Chaotic Dynamics
2009-11-10 v2 Dynamical Systems
Probability
Quantum Physics
Abstract
Quantum Iterated Function System on a complex projective space is defined by a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with conformal maps (relativistic boosts) on the Bloch sphere are discussed.
Cite
@article{arxiv.nlin/0312021,
title = {On Quantum Iterated Function Systems},
author = {Arkadiusz Jadczyk},
journal= {arXiv preprint arXiv:nlin/0312021},
year = {2009}
}
Comments
Latex, 12 pages, 3 figures. Added plot of numerical estimate of the averaged contraction parameter fro quantum octahedron over the whole range of the fuzziness parameter. Added a theorem and proof of the uniqueness of the invariant measure. At the very end added subsection on "open problems"