Resonances and transport in the sawtooth map
The paper obtains the very detailed investigation of the sawtooth map T of a cylinder on itself, which has a form \[ T(x,p)=(x+p+K(x-0.5),p+K(x- 0,5)),\quad (x,p)\in S^ 1\times {\mathbb{R}},\quad K\in {\mathbb{R}}^+. \] This map is considered as a model for chaotic Hamiltonian system. Analytical expressions are obtained for its cantori and resonances. The partial flux transferred from one resonance to another is determined by the degree of overlap of their turnstiles. The survival probability within a resonance is calculated using the Markov model. A construction of the horseshoe for trapped orbits is provided.
scientific article; zbMATH DE number 4190755