Dirichlet series for finite combinatorial rank dynamics
2010 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 362, no 1, 199-227 p.Article in journal (Refereed) Published
We introduce a class of group endomorphisms - those of finite combinatorial rank - exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is shown to to be a rational function of exponential variables. Analytic properties of the Dirichlet series are related to orbit-growth asymptotics: depending on the location of the abscissa of convergence and the degree of the pole there, various orbit-growth asymptotics are found, all of which are polynomially bounded.
Place, publisher, year, edition, pages
2010. Vol. 362, no 1, 199-227 p.
PRIME NUMBER THEOREM, PERIODIC POINTS, ZETA-FUNCTIONS, CLOSED ORBITS, SYSTEMS, AUTOMORPHISMS, SOLENOIDS, ENTROPY, SHIFTS, ANALOG
IdentifiersURN: urn:nbn:se:kth:diva-29065DOI: 10.1090/S0002-9947-09-04962-9ISI: 000273614300007ScopusID: 2-s2.0-77950870495OAI: oai:DiVA.org:kth-29065DiVA: diva2:392483
QC 201101272011-01-272011-01-252011-01-27Bibliographically approved