On the dynamical meaning of spectral dimensions
Annales de l'I.H.P. Physique théorique, Volume 68 (1998) no. 4, p. 491-506
@article{AIHPA_1998__68_4_491_0,
     author = {Guarneri, Italo},
     title = {On the dynamical meaning of spectral dimensions},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {68},
     number = {4},
     year = {1998},
     pages = {491-506},
     zbl = {0910.58031},
     mrnumber = {1634313},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1998__68_4_491_0}
}
Guarneri, Italo. On the dynamical meaning of spectral dimensions. Annales de l'I.H.P. Physique théorique, Volume 68 (1998) no. 4, pp. 491-506. http://www.numdam.org/item/AIHPA_1998__68_4_491_0/

[1] G. Casati, B.V. Chirikov, F.M. Izrailev and J. Ford, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, G. CSATI and J. FORD eds., Springer Lecture Notes in Physics 93 (1973). | MR 550884

[2] S. Fishman, DF.R. Grempel, and R.E. Prange, Phys. Rev. Lett. 49 (1982) 509. For a review of dynamical localization theory see, e.g., S. Fishman, in Proceedings of the 1991 Varenna Course CXIX, G. CASATI, I. GUARNERI and U. SMILANSKY eds., North-Holland 1993, p.187. | MR 669169

[3] B.V. Chirikov, F.M. Izrailev and D.L. Shepelyansky, Sov.Sci.Rev., Sect.C, 2, (1981),209. | MR 659270 | Zbl 0534.60096

[4] I. Guarneri, Europhys.Lett. 10 (1989) 95.

[5] An early discussion of singular continuous spectra in the context of quantum-classical instabilities appears in J. Bellisard, in Trends and Developments in the Eighties, S.Albeverio and P.Blanchard eds., World Scientific, Singapore (1985).

[6] G. Casati and I. Guarneri, Comm.Math.Phys. 95 (1984) 121. | MR 757057 | Zbl 0581.46062

[7] B. Simon, Annals of Math. 141 (1995) 131. | MR 1314033

[8] R. Lima and D. Shepelyansky, Phys.Rev.Lett. 67 (1991) 1377; T. Geisel, R. Ketzmerick and G. Petschel, ibid. 67 (1991) 3635; R. Artuso, G. Casati, and D.L. Shepelyansky, ibid. 68 (1992) 3826; R. Artuso, R. Borgonovi, I. Guarneri, L. Rebuzzini and G. Casati, ibid. 69 (1992) 3302.

[9] R. Borgonovi and I. Guarneri, Phys.Rev. B (1996).

[10] R. Ketzmerick, K. Kruse and T. Geisel, preprint Cond-Mat/9709054 (1997).

[11] R. Ketzmerick, G. Petschel, and T. Geisel, Phys. Rev.Lett. 69 (1992) 695; M. Holschneider, Commun.Math.Phys. 160 (1994) 457; J.M. Barbaroux, J.M. Combes, and R. Montcho, report CPT-96/P.3303, Marseille, 1996.

[12] J.M. Combes, in Differential Equations with applications to Mathematical Physics, edited by W. F. AMES, E. M. HARREL and J. V. HEROD (Academic, Boston 1993). | MR 1207142

[13] Y. Last, J.Funct.Anal. 142 (1995) 406. | MR 1423040 | Zbl 0905.47059

[14] R.S. Strichartz, J.Funct.Anal. 89 (1990) 154. | MR 1040961 | Zbl 0693.28005

[15] M. Wilkinson and E.J. Austin, Phys.Rev. B50, (1994) 1420.

[16] Y. Last, private communication.

[17] I. Guarneri and H. Schulz-Baldes, preprint, Como 1998.

[18] F. Piéchon, Phys. Rev. Lett. 76 (1996) 4372.

[19] G. Mantica, Physica D 109 (1997) 113. | Zbl 0925.58041

[20] J. Zhong, J. Bellisard, and R. Mosseri, J.Phys. (Cond. Matter) 7 (1995) 3507.

[21] P.R. Halmos, Lectures on Ergodic Theory, Chelsea (1956); I.O. Cornfeld, S.V. Fomin, and Ya.G. Sinai, Ergodic Theory, vol. 115 of Grundlehren der matematischen Wissenschaften in Einzeldarstellungen, Springer (1982). A review of classical "genericity" results in the light of recent results in abstract operator theory is given by O. Knill, Discr. Cont. Dynamical Systems 4 (1998) 33. | MR 97489 | Zbl 0073.09302

[22] O. Queffélec, Substitution Dynamical Systems - Spectral Analysis, Springer Lecture Notes in Mathematics 1294 (1987). | MR 924156 | Zbl 0642.28013

[23] E. Gutkin, Physica D 19 (1986) 311, and references therein. | MR 844706 | Zbl 0593.58016

[24] R. Artuso, G. Casati and I. Guarneri, to appear in Phys.Rev.E.

[25] U. Feudel, A.S. Pikovsky and M.A. Zaks, Phys. Rev. E 51 (1995) 1762; I. Guarneri and M. Di Meo, J.Phys. A: Math. Gen. 28 (1995) 2717, and references therein.

[26] I. Guarneri, J.Math.Phys. 37, 10 (1996) 5195. | MR 1411626 | Zbl 0894.46051

[27] R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys.Rev.Lett. 79 (1997) 1959. | MR 1471447 | Zbl 0944.81002

[28] R. Del Rio, S. Jitomirskaya, Y. Last and B. Simon, J. d'Analyse Mathématique, 69 (1996) 153. | Zbl 0908.47002