Escape from intermittent repellers- Periodic orbit theory for crossover from exponential to algebraic decay

Abstract

We apply periodic orbit theory to study the asymptotic distribution of escape times from an intermittent map. The dynamical zeta function exhibits a branch point which is associated with an asymptotic power law escape. By an analytic continuation technique we compute a zero of the zeta function beyond its radius of convergence leading to a pre-asymptotic exponential decay. The time of crossover from an exponential to a power law is also predicted. The theoretical predictions are confirmed by numerical simulation. Applications to conductance fluctuations in quantum dots are discussed.