The role of generalized Bowen-Franks groups (BF-groups) as topological conjugacy invariants for T automorphisms is studied. Using algebraic number theory, a link is established between equality of BFgroups for different automorphisms (BF -equivalence) and an identical position in a finite lattice (L-equivalence). Important cases of equivalence of the two conditions are proved. Finally, a topolo...

Indeed, Margulis [lo] announced that for the geodesic flow on a d-dimensional compact manifold of curvature 1 the number of periodic orbits 7 with (minimal) period r(1) I x is asymptotic to ecd-‘jx/(d 1)x. This result bears a striking resemblance to the prime number theorem. Parry and Pollicott [12], following earlier work by Bowen [2, 41, generalized Margulis’ theorem to weakly mixing Axiom A ...

Classical ergodic theory for integer-group actions uses entropy as a complete invariant for isomorphism of IID (independent, identically distributed) processes (a.k.a. product measures). This theory holds for amenable groups as well. Despite recent spectacular progress of Bowen, the situation for non-amenable groups, including free groups, is still largely mysterious. We present some illustrati...

We revisit the notion of statistical attractor defined by Ilyashenko. We argue to show that they are optimally defined to exist and to describe the asymptotical statistics of Lebesgue-almost all the orbits. We contribute to the theory, defining a minimality concept of α-observable statistical attractors and proving that the space is always full Lebesgue decomposable into pairwise disjoint sets ...

INTRODUCTION Bowen therapy is an established complementary therapy with anecdotal reports of effectiveness. However, there is limited published research to substantiate safety or effectiveness. This is a pilot study to explore the potential impact of Bowen therapy in chronic stroke. METHODS A case series of 14 people with chronic stroke were offered 13 sessions of Bowen therapy over a three-m...