TY - JOUR
T1 - The error term in the prime orbit theorem for expanding semiflows
AU - Tsujii, Masato
N1 - Publisher Copyright:
© Cambridge University Press, 2017.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - We consider suspension semiflows of angle-multiplying maps on the circle and study the distributions of periods of their periodic orbits. Under generic conditions on the roof function, we give an asymptotic formula on the number of prime periodic orbits with period . The error term is bounded, at least, by for arbitrarily small ϵ>0, where and are, respectively, the topological entropy and the maximal Lyapunov exponent of the semiflow.
AB - We consider suspension semiflows of angle-multiplying maps on the circle and study the distributions of periods of their periodic orbits. Under generic conditions on the roof function, we give an asymptotic formula on the number of prime periodic orbits with period . The error term is bounded, at least, by for arbitrarily small ϵ>0, where and are, respectively, the topological entropy and the maximal Lyapunov exponent of the semiflow.
UR - http://www.scopus.com/inward/record.url?scp=85010877225&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85010877225&partnerID=8YFLogxK
U2 - 10.1017/etds.2016.113
DO - 10.1017/etds.2016.113
M3 - Article
AN - SCOPUS:85010877225
SN - 0143-3857
VL - 38
SP - 1954
EP - 2000
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 5
ER -