We are interested in the computability of the invariant measures in a computable dynamical system. We construct two counter-examples. The first one has a unique SRB measure, which is not computable. The second one has no computable invariant measure at all. The systems are topological, i.e. continuous transformations on compact spaces, so they admit invariant measures. A topological dynamical s...

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...

We prove that for a class of Zd shifts of finite type, d > 1, any invariant measure which is not a measure of maximal entropy can be perturbed a small amount in the weak* topology to an invariant measure of higher entropy. Namely, there are no invariant measures which are strictly local maxima for the entropy function.

In this work, we demonstrate that the integral formula for a generalised Sato-Levine invariant is consistent in certain situations with Evans and Berger's fourth-order winding number. Also, found that, principle, one can derive analogous high-order numbers by which calculate entanglement of braids. The number Brunnian 4-braid calculated algebraically using cup product on cohomology finite regul...