The error term of the prime orbit theorem for expanding semiflows

2015/02/02 by Tsujii, Masato
#37C30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.00422

Abstract

We consider suspension semiflows of an angle multiplying map 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 π(T) of prime periodic orbits with period ≤ T. The error term is bounded, at least, by exp((1-\frac14\lceil χ_max/h_top\rceil+ε) h_\top T) in the limit T→ ∞ for arbitrarily small ε>0, where h_top and χ_max are respectively the topological entropy and the maximal Lyapunov exponent of the semiflow.

Related

• Prime orbit theorems for expanding Thurston maps
• A Prime Orbit Theorem for Self-Similar Flows and Diophantine Approximation
• Counting prime orbits in shrinking intervals for expanding Thurston maps
• Normal distribution of Lyapunov exponents of periodic orbits for expanding circle maps
• The horocycle flow at prime times