Dynamical systems generated by d > 2 commuting homeomorphisms (topological Zd-actions) contain within them structures on many scales, and in particular contain many actions of Zk for 1 6 k 6 d. Familiar dynamical invariants for homeomorphisms, like entropy and periodic point data, become more complex and permit multiple definitions. We briefly survey some of these and other related invariants i...

in this paper, the time-like hyperruled surfaces in the minkowski 4-space and their algebraicinvariants are worked. also some characteristic results are found about these algebraic invariants.

The Anosov-Katok method is one of the most powerful tools constructing smooth volume-preserving diffeomorphisms entropy zero with prescribed ergodic or topological properties. To measure complexity systems zero, invariants like slow have been introduced. In this article we develop several mechanisms facilitating computation and measure-theoretic diffeomorphisms.

We apply the entropy formalism to the study of the near-horizon geometry of extremal black p-brane intersections in D > 5 dimensional supergravities. The scalar flow towards the horizon is described in terms an effective potential given by the superposition of the kinetic energies of all the forms under which the brane is charged. At the horizon active scalars get fixed to the minima of the eff...

We introduce two additive invariants of output quantum channels. If the value of one these invariants is less than 1 then the logarithm of the inverse of its value is a positive lower bound for the regularized minimum entropy of an output quantum channel. We give a few examples in which one of these invariants is less than 1.

In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen’s sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by measure-preserving transformations on a standard probability space. We show here that these measure and topological entropy invariants both coincide with their classical...

We introduce two additive invariants of output quantum channels. If the value of one these invariants is less than 1 then the logarithm of the inverse of its value is a positive lower bound for the regularized minimum entropy of an output quantum channel. We give a few examples in which one of these invariants is less than 1.