Rectifying separated nets

Rectifying Separated Nets

In our earlier paper [BuK] (see also McMullen’s paper [M]), we constructed examples of separated nets in the plane R2 which are not biLipschitz equivalent to the integer lattice Z2. These examples gave a negative answer to a question raised by H. Furstenberg and M. Gromov. Furstenberg asked this question in connection with Kakutani equivalence for R2-actions, [F]. Return times for a section of ...

NETS AND SEPARATED S-POSETS

Nets, useful topological tools, used to generalize certainconcepts that may only be general enough in the context of metricspaces. In this work we introduce this concept in an $S$-poset, aposet with an action of a posemigroup $S$ on it whichis a very useful structure in computer sciences and interestingfor mathematicians, and give the the concept of $S$-net. Using $S$-nets and itsconvergency we...

nets and separated s-posets

nets, useful topological tools, used to generalize certainconcepts that may only be general enough in the context of metricspaces. in this work we introduce this concept in an $s$-poset, aposet with an action of a posemigroup $s$ on it whichis a very useful structure in computer sciences and interestingfor mathematicians, and give the the concept of $s$-net. using $s$-nets and itsconvergency we...

Equivalence Relations on Separated Nets Arising from Linear Toral Flows

In 1998, Burago-Kleiner and McMullen independently proved the existence of separated nets in R which are not bi-Lipschitz equivalent (BL) to a lattice. A finer equivalence relation than BL is bounded displacement after dilation (BDD). Separated nets arise naturally as return times to a section for minimal R-actions. We analyze the separated nets which arise via these constructions, focusing par...

CFTR, a rectifying, non-rectifying anion channel?