Bounded orbit injection equivalence is an equivalence relation defined on minimal free Cantor systems which is a candidate to generalize flip Kakutani equivalence to actions of the Abelian free groups on more than one generator. This paper characterizes bounded orbit injection equivalence in terms of a mild strengthening of Rieffel-Morita equivalence of the associated C*-crossed-product algebra...

Modern synchrotron light sources are pushing the limits of storage ring performance. Precise control of the electron beam orbit is critical for achieving design goals in these machines. A review of closed orbit control will be given, including an overview of the sources of orbit motion, a description of closed orbit correction and feedback algorithms, and a discussion of the pitfalls and limita...

This paper is about ‡ow-orbit equivalence, a topological analogue of even Kakutani equivalence. In addition to establishing many basic facts about this relation, we characterize the conjugacies of induced systems that can be extended to a ‡ow-orbit equivalence. We also describe the relationship between ‡ow-orbit equivalence and a distortion function of an orbit equivalence. We show that if the ...

We consider the action of a semigroup S on a standard space E. An orbit coupling of two probability measures on E is a coupling of these measures giving the largest possible weight to the event that the orbits of the two coordinates meet each other. We establish the existence of such orbit couplings for a large class of semigroups S. We also discuss some applications.

A k-orbit map is a map with k flag-orbits under the action of its automorphism group. We give a basic theory of k-orbit maps and classify them up to k 6 4. “Hurwitz-like” upper bounds for the cardinality of the automorphism groups of 2orbit and 3-orbit maps on surfaces are given. Furthermore, we consider effects of operations like medial and truncation on k-orbit maps and use them in classifyin...

the magnetoresistance of a one-dimensional electron gas in a metallic ferromagnetic nanowire containing two atomic-size domain walls has been investigated in the presence of spin-orbit interaction. the magnetoresistance is calculated in the ballistic regime, within the landauer-büttiker formalism. it has been demonstrated that the conductance of a magnetic nanowire with double domain walls can ...