Mathematics – Group Theory
Scientific paper
2010-06-26
Mathematics
Group Theory
17 pages
Scientific paper
The algebraic entropy h, defined for endomorphisms f of abelian groups G, measures the growth of the trajectories of non-empty finite subsets F of G with respect to f. We show that this growth can be either polynomial or exponential. The greatest f-invariant subgroup of G where this growth is polynomial coincides with the greatest f-invariant subgroup P(G,f) of G (named Pinsker subgroup of f) such that h(f|_P(G,f))=0. We obtain also an alternative characterization of P(G,f) from the point of view of the quasi-periodic points of f. This gives the following application in ergodic theory: for every continuous injective endomorphism g of a compact abelian group K there exists a largest g-invariant closed subgroup N of K such that g|_N is ergodic; furthermore, the induced endomorphism g' of the quotient K/N has zero topological entropy.
Bruno Anna Giordano
Dikranjan Dikran
No associations
LandOfFree
The Pinsker subgroup of an algebraic flow does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Pinsker subgroup of an algebraic flow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Pinsker subgroup of an algebraic flow will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-525647