Average Periodic Orbits Of Hyperbolic Flows

Dynamic system and ergodic theory is one of the most successful branch of mathematic in the 20th century. It also is an important part of nonlinear science.This paper addresses the understanding of asymptotic behaviour of periodic orbits for hyperbolic flows. With symbolic dynamics, hyperbolic flow can be modelled by suspended flow. By defining transfer operator, discussing its contractivity and using the properties of function, we derive the asymptotic expression of orbits averages for hyperbolic flows.