a b Figure 1 Phase space portraits of

(a) (b) Figure 1: Phase space portraits of the weakly chaotic kicked rotor with stochasticity parameter K = 2 (a), and of the strongly chaotic kicked rotor with K = 10 (b). S. Fishman and S. Rahav, Relaxation and Noise in Chaotic Systems, in Dynamics of Dissipation, Lecture Notes in Physics Vol. 597, (Springer-Verlag, Berlin Heidelberg 2002), Edited by P. Garbaczewski and R. Olkiewicz (Proceeding of “ 38 Winter School of Theoretical Physics: Dynamical Semigroups: Dissipation, Chaos, Quanta”, February 2002, Ladek, Poland)

Classical Accelerator Modes Figure 2: Phase portrait of the Standard map where (a) and (b) are sequences of island chains of the first and second generations, respectively, with periods 3 and 8 for K=K(1); (c) and (d) are the same as (a) and (b) for K=K(2) with period 5 for the first generation and 11 for the second one. A. Iomin, S. Fishman and G. M. Zaslavsky, Phys. Rev. E, 65, 036215 (2002)

Kicked Top Table 1: Eigenvalues of U(N) for t = 10. 2 truncated at lmax = 30, 40, 50 and 60 J. Weber, F. Haake, P. A. Braun, C. Manderfeld and P. Seba, J. Phys. A 34, 7195 (2001).

Kicked Top Figure 3: The eigenfunctions corresponding to the eigenvalues 0. 7696 (a), − 0. 3388±i 0. 6243 (b), − 0. 0058±i 0. 7080 (c), 0. 6480 (d) of U(N) for t = 10. 2, and lmax = 60. J. Weber, F. Haake, P. A. Braun, C. Manderfeld and P. Seba, J. Phys. A 34, 7195 (2001).

Kicked Top Figure 4: The decay of C(n) (dots) with ρ(0) corresponding to the eigenfunction shown in figure (b) of the previous slide. The numerical fit (line) yields a decay factor 0. 7706. J. Weber, F. Haake, P. A. Braun, C. Manderfeld and P. Seba, J. Phys. A 34, 7195 (2001).

Kicked rotor Figure 5: The fast relaxation rates g for various functions f and g with k=0 Figure 6: The diffusion coefficient D for K ≤ 20 M. Khodas, S. Fishman and O. Agam, Phys. Rev. E, 62, 4769 (2000). All the figures (except figure 2) and table can also be found at: S. Fishman and S. Rahav, Relaxation and Noise in Chaotic Systems, in Dynamics of Dissipation, Lecture Notes in Physics Vol. 597, (Springer-Verlag, Berlin Heidelberg 2002), Edited by P. Garbaczewski and R. Olkiewicz (Proceeding of “ 38 Winter School of Theoretical Physics: Dynamical Semigroups: Dissipation, Chaos, Quanta”, February 2002, Ladek, Poland).