Markov-Tree Model of Intrinsic Transport in Hamiltonian Systems

A particle in a chaotic region of phase space can spend a long time near the boundary of a regular region since transport there is slow. This "stickiness" of regular regions is thought to be responsible for previous observations in numerical experiments of a long-time algebraic decay of the particle survivial probability, i.e., survival probability $\sim t^{-z}$ for large $t$. This paper presents a global model for transport in such systems and demonstrates the essential role of the infinite hierarchy of small islands interspersed in the chaotic region. Results for $z$ are discussed.