Chapter 4
　　Here we focus on the measure-theoretic and fractal （ormultifractal） properties of the residual set of the local map. Theintroduction of Hausdorff dimension and Haus- dorff measure will beessential， later on， to formulating transport on interesting setsof Lebesgue measure zero. Using a transfer matrix to linksuccessive levels of the renormalization hierarchy， we calculate anontrivial spectrum of generalized dimensions for the π/7model.
　　Chapter 5
　　We now examine how the localreturn maps of a scaling sequence canbe lifted to the nfinite kicked-oscillator phase space. In somecases the resulting global translation vectors are globallyexpansive， increasing in length geometrically with increasinglevel. In such cases， we prove that the discontinuity-avoidingaperiodic orbits tend to infinity according to a power law. Westudy this phenomenon numerically in a number of examples. In theparticularly interesting case of the π/7 model， we see thatdifferent initial conditions can lead to a variety of asymptoticpower laws.
　　Chapter 6
　　A statistical formulation of the time evolution is presented inthis chapter， based on a coarse-grained probability distributionP（（m，n），t）. Once again， the renormaliz- ability of the models andespecially the recursive tiling property， serve as the organizingprinciples. We consider examples in which the probability issupported on the 2-dimensional periodic domains， but also onesrestricted to interesting lower- dimensional sets. Highly efficientcodometer updating allows us to investigate numerically asymptoticpower laws with log-periodic modulation.
　　Chapter 7
　　In this final chapter， we consider a different type of kickedoscillator dynamics， namely that of a Hamiltonian round-off map（Lowenstein et al， 1997; Lowenstein and Vivaldi， 1998， 2000）. Onceagain we have a local piecewise isometry which induces apermutation of 22. Although in this class of models all orbits areperiodic， one can still describe the long-time behaviorstatistically in terms of periodically and quasi-periodicallymodulated power laws. We study these both analytically and withhighly efficient numerical experiments.
　　Appendixes
　　For the sake of completeness， we include in the Appendix A anumber of data tables for the models which appear throughout thebook.ln addition， we have a short explanation of our implementationof the hierarchical symbolic dynamics， the codometer， in AppendixB.
　　……