Here we slow down in order to develop some fingertip feeling for the objects derived so far. This part is bedtime reading. A few special determinants are worked out by hand. Chapter 14 Thermodynamic formalism Generalized dimensions, entropies and such. 2000 Chapter 15 Discrete symmetries Dynamics often comes equipped with discrete symmetries, such as the reflection and the rotation symmetries.
Symmetries simplify and improve the cycle expansions in a rather beautiful way.
This chapter explains how symmetries factorize the cycle expansions. Exercises 10 jan 99 Chapter 16 Deterministic diffusion We look at transport coefficients and compute the diffusion constant. All done from first principles without ever invoking probability. This is what could have been done with the old quantum mechanics if physicists of 1910's were as familiar with chaos as you by now are. The Gutzwiller trace formula together with the corresponding spectral determinant, the central results of the semiclassical periodic orbit theory, are derived.