It is shown how the local structure of chaotic repellers, being responsible for transient chaotic behaviour, is deduced from the properties of hyperbolic periodic orbits. Relations between static and dynamical multifractal spectra, with respect to the natural invariant measure on the repeller, are derived for invertible maps of the plane. The results obtained for maps with unit Jacobian apply to Hamiltonian systems with two degrees of freedom which exhibit the phenomenon of irregular scattering and are characterised by an exponential decay of trapping probability.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)